1. Equations & Inequalities

Linear Equations

1. Equations & Inequalities

# Linear Equations - Video Tutorials & Practice Problems

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concept

## Introduction to Solving Linear Equtions

Video duration:

7mPlay a video:

2

Problem

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

A

$x=-27$

B

$x=-1$

C

$x=1$

D

$x=16$

3

concept

## Solving Linear Equations with Fractions

Video duration:

4mPlay a video:

4

Problem

ProblemSolve the equation.

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

A

$x=10$

B

$x=4$

C

$x=8$

D

$x=-1$

5

concept

## Categorizing Linear Equations

Video duration:

6mPlay a video:

6

Problem

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

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

A

Identity

B

Conditional

C

Inconsistent

7

Problem

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

A

Identity

B

Conditional

C

Inconsistent

8

Problem

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

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

A

Identity

B

Conditional

C

Inconsistent

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PRACTICE PROBLEMS AND ACTIVITIES (97)

- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1/x + 2 = 3/x
- In Exercises 1–26, solve and check each linear equation. 4x + 9 = 33
- Solve each equation. 2x+8 = 3x+2
- Solve each equation. 5x-2(x+4)=3(2x+1)
- In Exercises 1–26, solve and check each linear equation. 7x - 5 = 72
- Solve each equation. A= 24f / B(p+1), for f (approximate annual interest rate)
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. (x−2)/2x + 1 = (x+...
- Decide whether each statement is true or false. The solution set of 2x+5=x -3 is {-8}.
- Solve each problem. If x represents the number of pennies in a jar in an applied problem, which of the followi...
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 3/(x+1) = 5/(x−1)
- In Exercises 1–26, solve and check each linear equation. 11x - (6x - 5) = 40
- Decide whether each statement is true or false. The equation 5x=4x is an example of a contradiction.
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. (x−6)/(x+5) = (x−3...
- In Exercises 1–26, solve and check each linear equation. x - 5(x + 3) = 13
- In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 3x/4 - x/3 + 1 = ...
- Solve each equation. 5x+4= 3x-4
- In Exercises 1–26, solve and check each linear equation. 2x - 7 = 6 + x
- Solve each equation. 6(3x-1)= 8 - (10x-14)
- In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 4x-2(1-x)=3(2x+1)...
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1 − 4/(x+7) = 5/(x...
- In Exercises 1–26, solve and check each linear equation. 7x + 4 = x + 16
- In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equatio...
- In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x
- In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equatio...
- Solve each equation. 3x+5 - 5(x+1)= 6x+7
- In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equatio...
- Solve each equation. 4[2x-(3-x)+5] = -6x - 28
- In Exercises 1–26, solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 6/x − x/3 = 1
- Solve each equation. 1/15(2x+5) = 1/9(x+2)
- In Exercises 1–26, solve and check each linear equation. 2 - (7x + 5) = 13 - 3x
- Solve each equation. 0.2x - 0.5 = 0.1x+7
- In Exercises 1–26, solve and check each linear equation. 16 = 3(x - 1) - (x - 7)
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 1/x−1 + 1/x+1 = 2/...
- Solve each equation. 0.5x+ 4/3x= x+10
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/3 = x/2 - 2
- In Exercises 25-38, solve each equation. 20 - x/3=x/2
- Solve each equation. 0.08x+0.06(x+12) = 7.72
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 20 - x/3 = x/2
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 2/(x+3) − 5/(x+1) ...
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1
- Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution...
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 3y/(y²+5y+6) + 2/(...
- In Exercises 25-38, solve each equation. (x + 3)/6 = 2/3 + (x - 5)/4
- Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution...
- In Exercises 25-38, solve each equation. x/4 =2 +(x-3)/3
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8...
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 =...
- Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution...
- Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the...
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/...
- Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the val...
- Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the...
- Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the...
- Solve and check: 24 + 3 (x + 2) = 5(x − 12).
- Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the val...
- Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the val...
- Solve each equation for x. 2(x-a) +b =3x+a
- Solve each equation for x. ax+b=3(x-a)
- Solve each equation for x. x/a-1 = ax+3
- Solve each equation for x. a²x + 3x =2a²
- Solve: 2x(x+3)+6(x−3)=−28. (Section 5.7, Example 2)
- In Exercises 61–66, find all values of x satisfying the given conditions. y1 = 5(2x - 8) - 2, y2 = 5(x - 3) +...
- In Exercises 61–66, find all values of x satisfying the given conditions. y1 = (x - 3)/5, y2 = (x - 5)/4, and...
- In Exercises 61–66, find all values of x satisfying the given conditions. y1 = (2x - 1)/(x^2 + 2x - 8), y2 = ...
- In Exercises 67–70, find all values of x such that y = 0. y = 2[3x - (4x - 6)] - 5(x - 6)
- In Exercises 67–70, find all values of x such that y = 0. y = (x + 6)/(3x - 12) - 5/(x - 4) - 2/3
- In Exercises 67–70, find all values of x such that y = 0. y = 1/(5x + 5) - 3/(x + 1) + 7/5
- In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equ...
- In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equ...
- Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8
- Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominat...
- In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equ...
- The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each ...
- The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each ...
- The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each ...
- Retaining the Concepts. Solve and determine whether 8(x - 3) + 4 = 8x - 21 is an identity, a conditional equat...
- Evaluate x^2 - x for the value of x satisfying 4(x - 2) + 2 = 4x - 2(2 - x).
- In Exercises 99–106, solve each equation. [(3 + 6)^2 ÷ 3] × 4 = - 54 x
- In Exercises 99–106, solve each equation. 5 - 12x = 8 - 7x - [6 ÷ 3(2 + 5^3) + 5x]
- In Exercises 99–106, solve each equation. 0.7x + 0.4(20) = 0.5(x + 20)
- In Exercises 99–106, solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)
- Solve: 9(x − 1) = 1 + 3(x−2). (Section 1.4, Example 3)
- What is an identity equation? Give an example.
- What is a conditional equation? Give an example.
- What is an inconsistent equation? Give an example.
- Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.