Question 1

Solve the equation below for $$x$$:

$$\frac{x+6}{2} = 2 - \frac{x+6}{3}$$

What is the solution set?

Accepted Answer

$$\{6\}$$

Question 2

Which of the following is the first step to solve the equation $$\frac{x+6}{2} = 2 - \frac{x+6}{3}$$?

Accepted Answer

Multiply both sides by 6 to clear denominators.

Question 3

After multiplying both sides of $$\frac{x+6}{2} = 2 - \frac{x+6}{3} by 6$$, what is the resulting equation?

Accepted Answer

$$3(x+6) = 12 - 2(x+6)$$

Question 4

What is the value of $$x$$ that satisfies $$\frac{x+6}{2} = 2 - \frac{x+6}{3}$$?

Accepted Answer

$$6$$

Question 5

Which of the following best describes the solution set of $$\frac{x+6}{2} = 2 - \frac{x+6}{3}$$?

Accepted Answer

A single real number

Question 6

If you substitute $$x = 6$$ into the original equation $$\frac{x+6}{2} = 2 - \frac{x+6}{3}$$, what is the value of both sides?

Accepted Answer

$$6$$

Question 7

Which of the following is a common mistake when solving $$\frac{x+6}{2} = 2 - \frac{x+6}{3}$$?

Accepted Answer

Forgetting to multiply both sides by the least common denominator

Question 8

Which of the following real-world scenarios could be modeled by an equation of the form $$\frac{x+6}{2} = 2 - \frac{x+6}{3}$$?

Accepted Answer

Splitting a total cost between two people and subtracting a portion given to a third person

Question 9

If the equation $$\frac{x+6}{2} = 2 - \frac{x+6}{3}$$ had no solution, what would be true about the equation?

Accepted Answer

The variable terms would cancel and leave a false statement.

Question 10

Suppose you change the equation to $$\frac{x+6}{2} = 2 + \frac{x+6}{2}. $$What is the solution set?

Accepted Answer

$$\varnothing$$

Solving Linear Equations with Fractions

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