Question 1

What is the least common denominator (LCD) of the fractions $$\frac{n-1}{6}$$, $$\frac{n+1}{7}$$, and $$\frac{19}{21}$$?

Accepted Answer

$$42$$

Question 2

After multiplying both sides of the equation $$\frac{n-1}{6} + \frac{n+1}{7} = \frac{19}{21} by$$ $$42$$, what is the resulting equation?

Accepted Answer

$$7(n-1) + 6(n+1) = 2 \cdot 19$$

Question 3

Which property is used when expanding $$7(n-1) + 6(n+1)$$?

Accepted Answer

Distributive property

Question 4

What is the simplified form of $$7(n-1) + 6(n+1)$$?

Accepted Answer

Question 5

After combining like terms in $$7n - 7 + 6n + 6 = 38$$, what is the resulting equation?

Accepted Answer

$$13n - 1 = 38$$

Question 6

What is the value of $$n$$ after solving $$13n - 1 = 38$$?

Accepted Answer

$$n = 3$$

Question 7

Which step is necessary to clear the fractions in the equation $$\frac{n-1}{6} + \frac{n+1}{7} = \frac{19}{21}$$?

Accepted Answer

Multiply both sides by the LCD

Question 8

If you substitute $$n = 3$$ back into the original equation, what is the value of the left side?

Accepted Answer

$$\frac{2}{6} + \frac{4}{7}$$

Question 9

What is the purpose of multiplying both sides of an equation by the LCD?

Accepted Answer

To eliminate all fractions

Question 10

Which of the following is the correct sequence of steps to solve $$\frac{n-1}{6} + \frac{n+1}{7} = \frac{19}{21}$$?

Accepted Answer

Multiply by LCD, distribute, combine like terms, solve for $$n$$

Question 11

If the equation was $$\frac{n-1}{6} + \frac{n+1}{7} = \frac{20}{21}$$, what would be the new equation after multiplying both sides by $$42$$?

Accepted Answer

$$7(n-1) + 6(n+1) = 2 \cdot 20$$

Question 12

Which real-world scenario could be modeled by the equation $$\frac{n-1}{6} + \frac{n+1}{7} = \frac{19}{21}$$?

Accepted Answer

Two workers complete parts of a task at different rates, and their combined work equals a total amount.

Question 13

What is the result of applying the distributive property to $$6(n+1)$$?

Accepted Answer

$$6n + 6$$

Question 14

Which of the following is a common mistake when clearing fractions in equations?

Accepted Answer

Multiplying only one side by the LCD

Question 15

After solving $$13n = 39$$, what is the value of $$n$$?

Accepted Answer

$$n = 3$$

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

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