Question 1

Solve the linear equation below and select the correct solution set:

$$\frac{x+1}{16} = \frac{1}{8} + \frac{x-3}{9}$$

Accepted Answer

The solution set is $$\{4\}.$$

Question 2

Which of the following is the first step to solve the equation $$\frac{x+1}{16} = \frac{1}{8} + \frac{x-3}{9}$$?

Accepted Answer

Multiply both sides by the least common denominator of 16, 8, and 9.

Question 3

After clearing denominators in the equation $$\frac{x+1}{16} = \frac{1}{8} + \frac{x-3}{9}$$, which equation do you obtain?

Accepted Answer

$$9(x+1) = 18 + 16x - 48$$

Question 4

What is the least common denominator (LCD) of the denominators in the equation $$\frac{x+1}{16} = \frac{1}{8} + \frac{x-3}{9}$$?

Accepted Answer

$$144$$

Question 5

Suppose you solve $$\frac{x+1}{16} = \frac{1}{8} + \frac{x-3}{9}$$ and find $$x=4. $$Which of the following is the correct way to check your solution?

Accepted Answer

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

Question 6

If you mistakenly add $$\frac{x-3}{9} to $$both sides of $$\frac{x+1}{16} = \frac{1}{8} + \frac{x-3}{9}$$, which of the following equations do you get?

Accepted Answer

$$\frac{x+1}{16} + \frac{x-3}{9} = \frac{1}{8}$$

Question 7

Which of the following real-world scenarios can be modeled by a linear equation similar to $$\frac{x+1}{16} = \frac{1}{8} + \frac{x-3}{9}$$?

Accepted Answer

Mixing two solutions with different concentrations to achieve a target concentration.

Question 8

If the solution to a linear equation is $$x=4$$, which of the following statements is true?

Accepted Answer

The equation has exactly one solution.

Question 9

Which of the following best describes the solution set $$\varnothing$$?

Accepted Answer

No real number satisfies the equation.

Question 10

If you solve a linear equation and obtain a statement like $$0=0$$, what does this indicate about the solution set?

Accepted Answer

The solution set is all real numbers.

Solving Linear Equations with Fractions

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