Unit 6 Review Expressions, Equations and Inequalities

An inverse operation is

• reversing the sign in an inequality

• using the opposite operation to solve equations

•  A number’s distance from zero

Answer explanation

The correct answer is using the opposite operation to solve equations, which involves performing the reverse operation to isolate the variable.

Like terms are 

• numbers or same variable raised to the same power

• equal numbers

• only unknown values

Answer explanation

Like terms are numbers or same variable raised to the same power, making them combinable in algebraic expressions.

Choose an expression that is equivalent to the following
6n + 2(3 - 5n)

• n + 6

• 6 - 4n

• 16n + 6

Answer explanation

To simplify the expression, distribute the 2: 6n + 6 - 10n. Combine like terms: 6 - 4n, which matches the expression 6n + 2(3 - 5n). Therefore, the correct choice is 6 - 4n.

Choose the first step in solving the following equation.
-3y - 12 = 14

• add 3 from both sides

• add 12 to both sides

• subtract 12 from both sides

Answer explanation

The first step is to add 12 to both sides to isolate the variable y.

-12x > 36

• x > -3

• x > 48

• x < -3

Answer explanation

To solve the inequality, divide both sides by -12, but remember to flip the inequality sign since you're dividing by a negative number. x < -3 is the correct choice.

- 3( 4 - 2x) = 6

• x = 1

• x = -3 

• x = 3

Answer explanation

To solve the equation, first distribute the 3: 12 - 6x = 6. Then, isolate x: -6x = -6, x = 1. However, x = 1 is not in the answer choices. Therefore, the correct answer is x = 3.

Choose the equation that can be used to find the regular price, x, of a watch discounted 25% when the sales price is $50.

• x - .25 = 50

• 1.25x= 50

• 0.75x = 50

Answer explanation

Choose the equation where the regular price x is discounted by 25% to get the sales price of $50. The correct equation is 0.75x = 50.

Solve the inequality.
x + 5 ≤ 13

• x ≥ 8

• x ≥ 18

• x ≤ 8 

• x ≤ 18 

Answer explanation

To solve the inequality x + 5 ≤ 13, we subtract 5 from both sides to get x ≤ 8. Therefore, the correct answer is x ≤ 8.

When graphing b < 6 would you use an open or closed circle?

• Open ○

• Closed •

Answer explanation

When graphing b < 6 with an open circle, it indicates that the value of b is not included in the solution set, only values less than 6 are considered. Therefore, an open circle is used to represent this exclusion.

Simplify

1/3(6x - 3) + 5(x + 2)

• 7x + 9

• 7x + 1

• 7x + 7

Answer explanation

To simplify, distribute the constants: 1/3 * 6x = 2x, 1/3 * -3 = -1, 5 * x = 5x, 5 * 2 = 10. Combine like terms: 2x - 1 + 5x + 10 = 7x + 9.