Q: Solve the equation $$x + 6 = 15$$ and check your answer.

$$x = 9$$; \text{Check: } 9 + 6 = 15$

Q: Solve and check: $$2x + 5 = 27$$

$$x = 11$$; \text{Check: } 2 \times 11 + 5 = 27$

Q: Solve and check: $$4x + 3 = 51$$

$$x = 12$$; \text{Check: } 4 \times 12 + 3 = 51$

Question 1

Which of the following equations is a linear equation in one variable?

Accepted Answer

$$4x - 7 = 9$$

Question 2

What is the solution set for the equation $$x - 8 = 13$$?

Accepted Answer

$$\{21\}$$

Question 3

Which property allows you to add the same number to both sides of an equation without changing its solution?

Accepted Answer

Addition Property of Equality

Question 4

Solve the equation $$x + 6 = 15$$ and check your answer.

Accepted Answer

$$x = 9$$; 	ext{Check: } 9 + 6 = 15$

Question 5

Which of the following equations is NOT linear?

Accepted Answer

$$|x| + 2 = 8$$

Question 6

Solve for $$x in $$the equation $$3x - 5 = 16.$$

Accepted Answer

$$x = 7$$

Question 7

A child’s vocabulary $$V is $$modeled by $$V = 40A + 100$$ where $$A is $$age in months. What is the vocabulary size at $$A = 30$$ months?

Accepted Answer

$$V = 1200$$

Question 8

If $$x + 7 = 20$$, what is the value of $$x$$?

Accepted Answer

$$x = 13$$

Question 9

Which step is necessary to solve $$x - 4 = 10$$?

Accepted Answer

Add 4 to both sides

Question 10

Solve and check: $$2x + 5 = 27$$

Accepted Answer

$$x = 11$$; 	ext{Check: } 2 	imes 11 + 5 = 27$

Question 11

Which equation represents a real-world scenario modeled by a linear equation?

Accepted Answer

$$V = 40A + 100$$

Question 12

Solve for $$x in $$the equation $$5x - 2x = 9.$$

Accepted Answer

$$x = 3$$

Question 13

A medical researcher uses the formula $$V = 40A + 100 to $$estimate vocabulary. If a child has a vocabulary of 1700 words, what is their age in months?

Accepted Answer

$$A = 40$$

Question 14

Which of the following is the correct solution set for $$x - 5 = 12$$?

Accepted Answer

$$\{17\}$$

Question 15

Solve and check: $$4x + 3 = 51$$

Accepted Answer

$$x = 12$$; 	ext{Check: } 4 	imes 12 + 3 = 51$

Question 16

Which equation requires subtracting a variable term from both sides to isolate $$x$$?

Accepted Answer

$$2x - x = 7$$

Question 17

A child’s vocabulary is modeled by $$V = 40A + 100. If a $$child is 50 months old, what is their vocabulary size?

Accepted Answer

$$V = 2100$$

Question 18

Which of the following is a first-degree equation in $$x$$?

Accepted Answer

$$x + 7 = 14$$

Question 19

Solve for $$x in $$the equation $$7x + 2 = 81.$$

Accepted Answer

$$x = 11$$

Linear Equations in One Variable and the Addition Property of Equality

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