Two-Step Inequalities

Lesson 6-8:

Solve Two-Step Inequalities

Multiple Choice

Solve $$x-26>\ -29$$  

• x > 3

• x > -3

• x > 55

• x > -55

Multiple Choice

Solve $$-10\ge w+17$$  

• $$w\le-27$$  

• $$w\ge-27$$  

• $$w\le27$$  

• $$w\ge27$$  

Multiple Choice

Solve $$y-13\le6$$  

• $$y\le\ -19$$  

• $$y\le19$$  

• $$y\le7$$  

• $$y\le\ -7$$  

Multiple Choice

Solve $$\frac{r}{15}\ge-5$$  

• A

• B

• C

• D

Vocabulary

Two-Step Inequality - an inequality that contains two operations.

(Like two-step equations, you need to use the Inverse Order of Operations.)

Example: 3x + 4 ≥ 16

-4 -4

3x ≥ 12

3 3

x ≥ 4

Multiple Choice

You Try!

$$2x+8>24$$

• $$x>4$$

• $$x>8$$

• $$x\ge8$$

• $$x>14$$

Multiple Choice

When you graph an inequality, you use a closed dot when you use which symbols?

• ≤, ≥ 

• <, >

• ≤, <

• ≥, >

Multiple Choice

When graphing an inequality, you use an open dot when you use which symbol?

• <, >

• ≤, ≥ 

• ≤, <

• ≥, >

Multiple Choice

What would the graph to x > 8 look like?

• Open circle shaded to the left

• Open circle shaded to the right

• Closed circle shaded to the left

• Closed circle shaded to the right

Example: 7 - 2x > 11

-7 -7

-2x > 4

-2 -2

x < -2

Multiple Choice

What happens to the inequality sign when you divide by a negative number?

• It flips direction

• You add a line underneath

• Nothing happens.

Multiple Choice

Solve $$-8y\ge-64$$  

• $$y\ge8$$  

• $$y\le-8$$  

• $$y\ge-8$$  

• $$y\le8$$  

Multiple Choice

You Try!

$$6-3x\le9$$

• $$x\le-1$$

• $$x\ge-1$$

• $$x\le5$$

• $$x\ge5$$

Multiple Choice

Solve $$3x-9>21$$  

• $$x<30$$  

• $$x>30$$  

• $$x<10$$  

• $$x>10$$  

Multiple Choice

Solve $$-3x-4<14$$  

• $$x<-6$$  

• $$x>-6$$  

• $$x<6$$  

• $$x>6$$  

Multiple Choice

Solve $$\frac{y}{2}+6\ge10$$  

• $$y\ge4$$  

• $$y>4$$  

• $$y\ge8$$  

• $$y>8$$  

Multiple Choice

Solve $$6x-15\ge33$$  

• $$x\le8$$  

• $$x\ge3$$  

• $$x\le3$$  

• $$x\ge8$$  

Multiple Choice

Solve $$25\ge2a-9$$  

• $$a\le17$$  

• $$a\ge17$$  

• $$a\le8$$  

• $$a\ge8$$