1. Equations & Inequalities

Linear Equations

1. Equations & Inequalities

Linear Equations

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07:48

Introduction to Solving Linear Equtions

Solving Linear Equations with Fractions

Categorizing Linear Equations

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Definition of Linear Equation In One Variable

0:22

Definition of Linear Equation In One Variable

Solving Linear Equations Requiring the Multiplication of Binomials

Solving Two - Step Linear Equations, Another Example

An Intro to Solving Linear Equations: Solving some Basic Linear Equations

Solving Linear Equations

Solving Multi - Step Linear Equations

Solving Two - Step Linear Equations

❖ Solving a Linear System of Equations by Graphing ❖

An Intro to Solving Linear Equations: What Does it Mean to be a Solution?

Solving a Basic Linear Equation - Example 2

Solving a Basic Linear Equation - Example 3

Solving Linear Equations with Fractional Quantities

Solving Linear Equations - Example 1

Solving Linear Equations

Solving a Basic Linear Equation - Example 2

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Multiple Choice

Solve the Equation. $3\left(2-5x\right)=4x+25$

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Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation. $\frac{x}{4}+\frac16=\frac{x}{3}$

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Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$-2\left(5-3x\right)+x=7x-10$

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Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$5x+17=8x+12-3\left(x+4\right)$

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Multiple Choice

Solve the equation.

$\frac92+\frac14\left(x+2\right)=\frac34x$

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Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$5 x + 17 = 8 x + 12 - 3 (x + 4)$

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1/x + 2 = 3/x

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 4x + 9 = 33

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Textbook Question

Solve each equation. 2x+8 = 3x+2

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Textbook Question

Solve each equation. 5x-2(x+4)=3(2x+1)

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 7x - 5 = 72

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Textbook Question

Solve each equation. A= 24f / B(p+1), for f (approximate annual interest rate)

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. (x−2)/2x + 1 = (x+1)/x

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Textbook Question

Decide whether each statement is true or false. The solution set of 2x+5=x -3 is {-8}.

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Textbook Question

Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the following equations cannot be a correct equation for finding x? (Hint:Solve the equations and consider the solutions.) A. 5x+3 =11 B.12x+6 =-4 C.100x =50(x+3) D. 6(x+4) =x+24

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 3/(x+1) = 5/(x−1)

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 11x - (6x - 5) = 40

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Textbook Question

Decide whether each statement is true or false. The equation 5x=4x is an example of a contradiction.

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. (x−6)/(x+5) = (x−3)/(x+1)

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Textbook Question

In Exercises 1–26, solve and check each linear equation. x - 5(x + 3) = 13

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Textbook Question

In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 3x/4 - x/3 + 1 = 4x/5 - 3/20

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Textbook Question

Solve each equation. 5x+4= 3x-4

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 2x - 7 = 6 + x

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Textbook Question

Solve each equation. 6(3x-1)= 8 - (10x-14)

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Textbook Question

In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 4x-2(1-x)=3(2x+1)-5

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1 − 4/(x+7) = 5/(x+7)

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 7x + 4 = x + 16

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Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x-5 = 7

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x

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Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2

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Textbook Question

Solve each equation. 3x+5 - 5(x+1)= 6x+7

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Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2(x-4)+3(x+5)=2x-2

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Textbook Question

Solve each equation. 4[2x-(3-x)+5] = -6x - 28

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 6/x − x/3 = 1

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Textbook Question

Solve each equation. 1/15(2x+5) = 1/9(x+2)

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 2 - (7x + 5) = 13 - 3x

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Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7x + 13 = 2(2x-5) + 3x + 23

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Textbook Question

Solve each equation. 0.2x - 0.5 = 0.1x+7

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Textbook Question

In Exercises 1–26, solve and check each linear equation. 16 = 3(x - 1) - (x - 7)

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1/x−1 + 1/x+1 = 2/x²−1

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Textbook Question

Solve each equation. 0.5x+ 4/3x= x+10

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Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. (3x+1)/3 - 13/2 = (1-x)/4

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Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/3 = x/2 - 2

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Textbook Question

In Exercises 25-38, solve each equation. 20 - x/3=x/2

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Textbook Question

Solve each equation. 0.08x+0.06(x+12) = 7.72

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Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 20 - x/3 = x/2

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Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 2/(x+3) − 5/(x+1) = (3x+5)/(x²+4x+3)

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Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1

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Textbook Question

Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. 1/2(6x+20) = x+4 +2(x+3)

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Textbook Question

In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 3y/(y²+5y+6) + 2/(y²+y−2) = 5y/(y²+2y−3)

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Textbook Question

In Exercises 25-38, solve each equation. (x + 3)/6 = 2/3 + (x - 5)/4

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Textbook Question

Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. 2(x-8) = 3x-16

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Textbook Question

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0

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Textbook Question

In Exercises 25-38, solve each equation. x/4 =2 +(x-3)/3

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Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8 + (x - 5)/4

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Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 = (x + 3)/8

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Textbook Question

Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. -0.6(x-5)+0.8(x-6) = 0.2x - 1.8

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Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. I=Prt,for P (simple interest)

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Textbook Question

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

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Textbook Question

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 4/x = 5/2x + 3

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Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. P=2l+2w,for w (perimeter of a rectangle)

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Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. F = GMm/r², for m (force of gravity)

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Textbook Question

Solve and check: 24 + 3 (x + 2) = 5(x − 12).

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Textbook Question

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. s = 1/2gt², for g (distance traveled by a falling object)

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

Solve each equation for x. 2(x-a) +b =3x+a

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Textbook Question

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Textbook Question

Solve each equation for x. ax+b=3(x-a)

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Textbook Question

Solve each equation for x. x/a-1 = ax+3

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Textbook Question

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Textbook Question

Solve each equation for x. a²x + 3x =2a²

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Textbook Question

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Textbook Question

Solve: 2x(x+3)+6(x−3)=−28. (Section 5.7, Example 2)

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Textbook Question

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = 5(2x - 8) - 2, y2 = 5(x - 3) + 3, and y1 = y2.

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Textbook Question

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = (x - 3)/5, y2 = (x - 5)/4, and y1 - y2 = 1.

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Textbook Question

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = (2x - 1)/(x^2 + 2x - 8), y2 = 2/(x + 4), y3 = 1/(x - 2), and y1 + y2 = y3.

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Textbook Question

In Exercises 67–70, find all values of x such that y = 0. y = 2[3x - (4x - 6)] - 5(x - 6)

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Textbook Question

In Exercises 67–70, find all values of x such that y = 0. y = (x + 6)/(3x - 12) - 5/(x - 4) - 2/3

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Textbook Question

In Exercises 67–70, find all values of x such that y = 0. y = 1/(5x + 5) - 3/(x + 1) + 7/5

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Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x + 7 = 7(x + 1) - 3x

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Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) = 21 + 4x

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Textbook Question

Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8

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Textbook Question

Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).

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Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 10x + 3 = 8x + 3

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Textbook Question

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7

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Textbook Question

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)

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Textbook Question

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Textbook Question

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Textbook Question

Retaining the Concepts. Solve and determine whether 8(x - 3) + 4 = 8x - 21 is an identity, a conditional equation, or an inconsistent equation.

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Textbook Question

Evaluate x^2 - x for the value of x satisfying 4(x - 2) + 2 = 4x - 2(2 - x).

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Textbook Question

In Exercises 99–106, solve each equation. [(3 + 6)^2 ÷ 3] × 4 = - 54 x

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Textbook Question

In Exercises 99–106, solve each equation. 5 - 12x = 8 - 7x - [6 ÷ 3(2 + 5^3) + 5x]

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Textbook Question

In Exercises 99–106, solve each equation. 0.7x + 0.4(20) = 0.5(x + 20)

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Textbook Question

In Exercises 99–106, solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)

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Textbook Question

Solve: 9(x − 1) = 1 + 3(x−2). (Section 1.4, Example 3)

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Textbook Question

What is an identity equation? Give an example.

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Textbook Question

What is a conditional equation? Give an example.

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Textbook Question

What is an inconsistent equation? Give an example.

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Textbook Question

Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.

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1. Equations & Inequalities

Linear Equations

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