Question 1

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

Accepted Answer

Multiply both sides by $$\displaystyle 12 to $$eliminate fractions.

Question 2

Solve the equation $$\displaystyle 2(x-3) = 0. $$What is the value of $$\displaystyle x$$?

Accepted Answer

$$\displaystyle x = 3$$

Question 3

A chemist is preparing a solution and needs to solve $$\displaystyle 3(2-5x) = 4x + 25 to $$determine the amount of a substance to add. What is the value of $$\displaystyle x$$?

Accepted Answer

$$\displaystyle x = -1$$

Question 4

Which of the following best describes the equation $$\displaystyle x = x + 4$$?

Accepted Answer

It is inconsistent and has no solution.

Question 5

After distributing and combining like terms, you obtain $$\displaystyle 0 = 0$$ when solving a linear equation. What does this indicate about the equation?

Accepted Answer

It is an identity and has infinitely many solutions.

Question 6

Solve the equation $$\displaystyle \frac{x}{4} + \frac{1}{6} = \frac{x}{3}. $$What is the solution set?

Accepted Answer

$$\displaystyle \{ -1 \}$$

Question 7

A medical researcher is analyzing a linear relationship between dosage $$\displaystyle x$$ and patient response. The equation $$\displaystyle 9 = 2 + \frac{1}{4}(x+2) = \frac{3}{4}x is $$used. What is the correct first step to solve for $$\displaystyle x$$?

Accepted Answer

Multiply both sides by $$\displaystyle 4 to $$eliminate fractions.

Question 8

Solve the equation $$\displaystyle 5x + 17 = 8x + 12 - 3(x+4). $$Then, categorize the equation.

Accepted Answer

Conditional; $$\displaystyle x = 3$$

Question 9

Which operation should be performed first when solving $$\displaystyle 3(x+2) - 4 = 2x + 5$$?

Accepted Answer

Distribute the $$\displaystyle 3 to$$ $$\displaystyle (x+2)$$

Question 10

A business calculates profit using the equation $$\displaystyle 2x + 4 = 10. $$What is the value of $$\displaystyle x$$?

Accepted Answer

$$\displaystyle x = 3$$

Question 11

Solve the equation $$\displaystyle -2(5-3x) + x = 7x - 10. $$What is the value of $$\displaystyle x$$?

Accepted Answer

$$\displaystyle x = 0$$

Question 12

Which of the following best describes the solution set for the equation $$\displaystyle x + 5 = x + 2 + 3$$?

Accepted Answer

Identity; all real numbers

Question 13

A student solves $$\displaystyle 2x + 3 = 2x + 5$$ and gets $$\displaystyle 3 = 5. $$What does this indicate about the equation?

Accepted Answer

It is inconsistent and has no solution.

Question 14

Which of the following is NOT a valid step when solving a linear equation with fractions?

Accepted Answer

Divide both sides by the least common denominator (LCD).

Question 15

Solve for $$\displaystyle x$$: $$\displaystyle 3x = 12$$

Accepted Answer

$$\displaystyle x = 4$$

Question 16

A recipe requires that the sum of $$\displaystyle x$$ and $$\displaystyle 2$$ equals $$\displaystyle 0. $$What is the value of $$\displaystyle x$$?

Accepted Answer

$$\displaystyle x = -2$$

Question 17

Which of the following is the correct solution to $$\displaystyle \frac{1}{4}(x+2) - \frac{1}{3}x = \frac{1}{12}$$?

Accepted Answer

$$\displaystyle x = 2$$

Question 18

When solving a linear equation, why must you perform the same operation on both sides?

Accepted Answer

To maintain the equality of the equation.

Question 19

A scientist is modeling a reaction with the equation $$\displaystyle 4x - 7 = 2x + 5. $$What is the value of $$\displaystyle x$$?

Accepted Answer

$$\displaystyle x = 6$$

Solving Linear Equations: Methods, Examples, and Classification

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