Question 1

Which of the following is a linear equation in one variable $$x$$?

Accepted Answer

$$x + 2 - 5 = 0$$

Question 2

Which of the following statements is an equation?

Accepted Answer

$$x - 3 + 2 - 4 = 4x$$

Question 3

Identify the error in the following solution:

$$8(x - 3) - 3(x - 3) = x + 5$$

$$8x - 24 - 3x - 9 = x + 5$$

$$2x - 9 = x + 5$$

$$x = 14$$

What was the mistake?

Accepted Answer

A sign error was made when applying the distributive property. The left side should be $$8x - 24 - 3x + 9.$$

Question 4

Solve the equation and determine the type of solution:

$$4x + 6 = 2$$

Accepted Answer

The solution set is $$x = -1$$

Question 5

Solve for $$x$$ and check your solution:

$$6x - 3 = 5x - 10 + 2x$$

Accepted Answer

The solution set is $$x = -7$$

Question 6

Which equation below is a contradiction?

Accepted Answer

$$x + 6 = x + 7$$

Question 7

Solve the equation and check the solution:

$$-8(v + 3) + 4v + 7 = 7v + 7$$

Accepted Answer

The solution set is $$v = -13$$

Question 8

A chemist is mixing two solutions. The equation $$\frac{x - 8}{3} + \frac{8}{3x} = 7$$ models the total concentration. What is the value of $$x$$?

Accepted Answer

$$x = 7$$

Question 9

Solve for $$x$$:

$$\frac{3x + 24}{5} + \frac{x + 21}{4} = 16$$

Accepted Answer

$$x = 7$$

Question 10

To solve the equation $$\frac{x - 17}{6} = \frac{7}{11}$$, what is the least common denominator (LCD) you should use?

Accepted Answer

$$66$$

Question 11

A medical researcher is analyzing a solution using the equation $$0.12y + 0.03y + 9000 = 1470. $$What is the least power of 10 you should multiply both sides by to clear decimals?

Accepted Answer

$$1000$$

Question 12

Solve for $$x$$ and check your solution:

$$\frac{1}{11}x = -\frac{5}{11}$$

Accepted Answer

$$x = -5$$

Question 13

Which of the following is an expression, not an equation?

Accepted Answer

$$x^2 + 4 - 4 + 4$

Question 14

Solve for $$x$$:

$$\frac{x - 40}{5} - \frac{x}{6} = -\frac{1}{3}$$

Accepted Answer

$$x = -72$$

Question 15

A business owner splits profits using the equation $$\frac{3x}{14} + \frac{5x}{7} = 13. $$What is the value of $$x$$?

Accepted Answer

$$x = 14$$

Question 16

Solve for $$x$$:

$$(2x + 3) - \frac{1}{3}(x + 6) = 4$$

Accepted Answer

$$x = 9$$

Question 17

Which of the following equations is an identity?

Accepted Answer

$$x - 8 = x - 8$$

Question 18

Solve for $$z$$:

$$[z - 10] - 15 + 4z = 4 + 4z + 10$$

Accepted Answer

$$z = 10$$

Question 19

A student solves $$x - 3 + 2 - 4 = 4x$$ and gets $$x = -1. $$What is the correct classification of this equation?

Accepted Answer

It is an equation because there is an equality symbol.

Question 20

Solve for $$x$$:

$$x + 8 - 3 = x + 11$$

Accepted Answer

Intermediate Algebra: Linear Equations, Expressions, and Solution Sets – Step-by-Step Guidance

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