Question 1

What is the first step to solve the equation $$\frac{9t}{20} - \frac{t}{5} = 1$$?

Accepted Answer

Multiply both sides by the least common denominator (LCD) of 20 and 5

Question 2

What is the least common denominator (LCD) of 20 and 5?

Accepted Answer

$$20$$

Question 3

After multiplying both sides of $$\frac{9t}{20} - \frac{t}{5} = 1 by 20$$, what is the resulting equation?

Accepted Answer

$$9t - 4t = 20$$

Question 4

Which property is used when you multiply both sides of an equation by the LCD?

Accepted Answer

Distributive property

Question 5

What is the value of $$t$$ that solves $$9t - 4t = 20$$?

Accepted Answer

$$t = 4$$

Question 6

After combining like terms in $$9t - 4t = 20$$, what is the equation?

Accepted Answer

$$5t = 20$$

Question 7

What is the final step to solve for $$t in$$ $$5t = 20$$?

Accepted Answer

Divide both sides by 5

Question 8

How do you check if $$t = 4 is a $$solution to $$\frac{9t}{20} - \frac{t}{5} = 1$$?

Accepted Answer

Substitute $$t = 4$$ into the original equation and verify both sides are equal

Question 9

When checking $$t = 4 in$$ $$\frac{9t}{20} - \frac{t}{5} = 1$$, what is $$\frac{9 	imes 4}{20}$$?

Accepted Answer

$$\frac{36}{20}$$

Question 10

What is $$\frac{4}{5}$$ written with a denominator of 20?

Accepted Answer

$$\frac{16}{20}$$

Question 11

After substituting $$t = 4$$ and rewriting with the LCD, what is $$\frac{36}{20} - \frac{16}{20}$$?

Accepted Answer

$$\frac{20}{20}$$

Question 12

What does $$\frac{20}{20}$$ simplify to?

Accepted Answer

$$1$$

Question 13

Why is $$t = 4$$ the solution to $$\frac{9t}{20} - \frac{t}{5} = 1$$?

Accepted Answer

Because substituting $$t = 4$$ makes both sides of the equation equal

Question 14

Which of the following is a correct step in clearing fractions from an equation?

Accepted Answer

Multiply both sides by the LCD of all denominators

Question 15

If you have $$\frac{a}{b} = c$$, what is the first step to solve for $$a$$?

Accepted Answer

Multiply both sides by $$b$$

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

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