Question 1

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

Accepted Answer

$$4x + 5 = 13$$

Question 2

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

Accepted Answer

$$x = 2$$

Question 3

A restaurant bill is $$48$$ dollars. You and a friend have a coupon for $$10$$ dollars off, and there is a $$10\%$$ tax added after the coupon is applied. If you split the final bill evenly, how much does each person pay? (Let $$x be $$the amount each pays.)

Accepted Answer

$$x = 20.90$$

Question 4

Which of the following is the correct first step to solve the equation $$\frac{1}{3}x - \frac{1}{4}x = 16$$?

Accepted Answer

Multiply both sides by $$12 to $$clear fractions.

Question 5

Simplify and solve: $$-4x - 1 + 5x = 9x + 3 - 7x.$$

Accepted Answer

$$x = 2$$

Question 6

Which property of equality justifies the following step: If $$a + b = c$$, then $$a + b - b = c - b$$?

Accepted Answer

Addition Property of Equality

Question 7

Solve for $$c in $$the equation $$0.6 = 2 - 3.5c.$$

Accepted Answer

$$c = 0.4$$

Question 8

Which of the following equations is an identity?

Accepted Answer

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

Question 9

What is the solution to the equation $$2(x - 3) = 5x - 9$$?

Accepted Answer

$$x = 1$$

Question 10

A chemist needs to prepare $$100 mL of a$$ $$30\%$$ saline solution by mixing a $$20\%$$ solution and a $$50\%$$ solution. Let $$x be $$the amount (in mL) of the $$20\%$$ solution used. Which equation represents this scenario?

Accepted Answer

$$0.2x + 0.5(100 - x) = 30$$

Question 11

Which of the following equations is a contradiction (has no solution)?

Accepted Answer

$$x + 2 = x + 5$$

Question 12

Solve for $$x$$: $$x + 5^2$ + 12 = 2x - x - 38.$$

Accepted Answer

$$x = -25$$

Question 13

Which step is incorrect in the following solution to $$3x - 5 = 16$$?

$$3x - 5 = 16$$
$$3x = 11$$
$$3x3 = 113$$
$$x = 113$$

Accepted Answer

Multiplying both sides by $$3$$

Question 14

Solve for $$x$$: $$0.3x + 0.1 = 0.27x - 0.02.$$

Accepted Answer

$$x = -0.5$$

Question 15

Which of the following best describes the equation $$4x + 2 = 4x + 2$$?

Accepted Answer

Identity

Question 16

A patient is prescribed a medication that requires the equation $$0.5x + 2 = 5 to $$determine the correct dosage $$x in mg. $$What is the correct dosage?

Accepted Answer

$$x = 3$$

Question 17

Which of the following is the correct next step after distributing in the equation $$2(x - 3) = 5x - 9$$?

Accepted Answer

Subtract $$2x$$ from both sides

Question 18

If $$3x + 5 = 3(x + 2)$$, what type of equation is this?

Accepted Answer

Contradiction

Question 19

Which of the following is the best strategy to solve an equation with decimals, such as $$0.3x + 0.1 = 0.27x - 0.02$$?

Accepted Answer

Multiply both sides by $$100 to $$clear decimals

Question 20

Which of the following is NOT a valid step when solving a linear equation in one variable?

Accepted Answer

Multiplying both sides by zero

Solving Linear Equations in One Variable

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