Question 1

What is the first step to solve the equation $$\frac{x}{9} + \frac{x}{5} = \frac{5}{18}$$?

Accepted Answer

Multiply both sides by the LCD of all fractions.

Question 2

What is the least common denominator (LCD) of the fractions in the equation $$\frac{x}{9} + \frac{x}{5} = \frac{5}{18}$$?

Accepted Answer

$$90$$

Question 3

After multiplying both sides of $$\frac{x}{9} + \frac{x}{5} = \frac{5}{18} by $$the LCD, what is the resulting equation?

Accepted Answer

$$10x + 18x = 25$$

Question 4

Which property is used to isolate $$x in $$the equation $$28x = 25$$?

Accepted Answer

Multiplication property of equality

Question 5

What is the solution to the equation $$\frac{x}{9} + \frac{x}{5} = \frac{5}{18}$$?

Accepted Answer

$$x = \frac{25}{28}$$

Question 6

When checking the solution $$x = \frac{25}{28} in $$the original equation, what is the value of $$\frac{x}{9} + \frac{x}{5}$$?

Accepted Answer

$$\frac{5}{18}$$

Question 7

Which of the following best describes the purpose of multiplying both sides of an equation by the LCD?

Accepted Answer

To eliminate fractions from the equation

Question 8

If $$a = b$$ and $$c 
eq 0$$, which property allows you to conclude $$ac = bc$$?

Accepted Answer

Multiplication property of equality

Question 9

Which step is necessary to verify that your solution to a linear equation is correct?

Accepted Answer

Substitute the solution back into the original equation

Question 10

Suppose you have the equation $$\frac{x}{4} + \frac{x}{6} = 5. $$What is the LCD of the fractions?

Accepted Answer

$$12$$

Question 11

After clearing fractions and combining like terms, you have $$7x = 21. $$What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 12

Which of the following is a correct application of the distributive property?

Accepted Answer

$$a(b + c) = ab + ac$$

Question 13

If you multiply both sides of $$\frac{x}{3} + \frac{x}{4} = 7 by $$the LCD, what equation do you get?

Accepted Answer

$$4x + 3x = 84$$

Question 14

Which of the following is NOT a valid step in solving $$\frac{x}{2} + \frac{x}{3} = 5$$?

Accepted Answer

Adding the denominators together

Question 15

A chemist needs to solve $$\frac{x}{7} + \frac{x}{2} = 9 to $$find the amount of a substance. What is the first step?

Accepted Answer

Multiply both sides by $$14$$

Solving Linear Equations with Fractions: Step-by-Step Guide

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