Question 1

Which of the following is the correct first step to solve the equation $$\frac{1}{4}x - \frac{2}{3} = \frac{5}{12}x$$?

Accepted Answer

Multiply both sides by 12 to clear the denominators.

Question 2

Solve for $$x$$: $$\frac{x}{3} + 3 = \frac{x}{5} - \frac{1}{3}.$$

Accepted Answer

$$x = -25$$

Question 3

What is the least common denominator (LCD) for the equation $$\frac{x}{8} + \frac{1}{4} = \frac{x}{4} + \frac{1}{2}$$?

Accepted Answer

$$8$$

Question 4

Which of the following is a correct application of the multiplication principle to clear fractions in $$\frac{1}{3}(x-2) = \frac{1}{5}(x+4) + 2$$?

Accepted Answer

Multiply both sides by 15.

Question 5

Solve for $$x$$: $$0.2(1 - 8x) + 1.1 = -5(0.4x - 0.3).$$

Accepted Answer

$$x = \frac{1}{2}$$

Question 6

Which of the following equations has no solution?

Accepted Answer

$$5(x+3) = 2x - 8 + 3x$$

Question 7

Which of the following equations has an infinite number of solutions?

Accepted Answer

$$9x - 8x - 7 = 3 + x - 10$$

Question 8

What is the correct procedure to solve an equation with fractions?

Accepted Answer

Multiply all terms by the LCD, combine like terms, isolate the variable, and check the solution.

Question 9

Solve for $$x$$: $$\frac{5x}{4} - 1 = \frac{3x}{4} + \frac{1}{2}.$$

Accepted Answer

$$x = 3$$

Question 10

Which of the following is NOT a valid step when solving $$\frac{x+2}{8} = \frac{x+1}{4}$$?

Accepted Answer

Divide both sides by 2 to get $$\frac{x+2}{4} = \frac{x+1}{2}.$$

Question 11

A chemist is mixing two solutions. The equation $$\frac{1}{2}(x+5) = \frac{1}{5}(x-2) + \frac{1}{2}$$ models the amount of a chemical in the mixture. What is the value of $$x$$?

Accepted Answer

$$x = -3$$

Question 12

Which of the following best explains why $$\frac{x+2}{8} = \frac{x+1}{4}$$ cannot be simplified to $$\frac{x+2}{4} = x+1$$?

Accepted Answer

You cannot divide out part of an addition or subtraction problem in the numerator.

Question 13

Solve for $$x$$: $$\frac{x+6}{9} = \frac{x}{6} + \frac{1}{2}.$$

Accepted Answer

$$x = -3$$

Question 14

A medical researcher is analyzing a dosage equation: $$\frac{1}{3}(x-2) = \frac{1}{5}(x+4) + 2. $$What is the correct value of $$x$$?

Accepted Answer

$$x = 26$$

Question 15

Which step is necessary to check your solution after solving an equation?

Accepted Answer

Substitute your solution back into the original equation.

Question 16

If you solve an equation and end up with a statement like $$-11 = 3$$, what does this mean?

Accepted Answer

The equation has no solution.

Question 17

If you solve an equation and end up with a statement like $$18 = 18$$, what does this mean?

Accepted Answer

The equation has an infinite number of solutions.

Question 18

Which of the following is the correct way to clear decimals in the equation $$0.2(1-8x) + 1.1 = -5(0.4x-0.3)$$?

Accepted Answer

Multiply both sides by 10.

Question 19

A student claims that $$\frac{x+2}{8} = \frac{x+1}{4}$$ can be simplified to $$\frac{x+2}{4} = x+1. Is $$this correct? Why or why not?

Accepted Answer

No, because you cannot divide out part of an addition or subtraction problem in the numerator.

Solving Linear Equations with Fractions and Decimals

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