Solving Equations & Inequalities

Review of Solving Equations

• To solve equations we must isolate the variable.

• To isolate the variable we use inverse operations.

• When solving equations with parentheses, you should distribute first. Then, use inverse operations.

• Always combine like terms on the same side of the equal sign before using inverse operations.

Dropdown

The goal when solving equations is to isolate the ​​

Select answer

.

Dropdown

To isolate the variable, we must use ​

Select answer

operations.

Fill in the Blanks

Solve the following equation.

$-14+2x=-6$  

x =

Multiple Choice

Solve the following equation.

$$28-4\left(3x+1\right)=0$$  

• x = 0

• x = 2

• x = 6

• x = -2

Fill in the Blanks

Solve the following equation.

$-16-3x=5x+24$  

x =

Multiple Choice

True or False.

To solve the equation below the first step could be to subtract 21x from both sides. $$21x-30=14x+5$$  

• True

• False

Intro to Algebraic Inequalities

Match

Match the following inequalities with their written equivalent.

• $$x\ \le-2$$  

• $$x\ge-2$$  

• $$x<-2$$  

• $$x>-2$$  

x is less than or equal to -2

x is greater than or equal to -2

x is less than -2

x is greater than -2

• x is less than or equal to -2

• x is greater than or equal to -2

• x is less than -2

• x is greater than -2

Multiple Choice

True or False.

-2 is a possible solution for $$x>-4$$  

• True

• False

Inequality Solutions

Inequality solutions can be represented on a number line.

Recall from previous year...

When shading > and < solutions,

leave the circle open.

Dropdown

Which inequality matches the number line below?



x ​

Select answer

5

Multiple Select

Which TWO of the following would we graph as OPEN circles?

• x < 5

• x < 5

• x > 5

• x > 5

Multiple Select

Which TWO of the following would we graph as CLOSED circles?

• x < 12

• x < 12

• x > 12

• x > 12

Multiple Choice

Which of the following represents

x > 1



To see the image better, click the image

• A

• B

• C

• D

Multiple Choice

Which of the following represents

x < 4

To see the image better, click the image

• A

• B

• C

• D

Multiple Choice

Which of the following represents

x > 5

• A

• B

• C

• D

Draw

Graph the inequality X < -17

Solving Algebraic Inequalities

• ​To solve inequalities, we will still use inverse operations.

• The solution to an inequalities is considered a solution set.

Multiple Choice

Solve the inequality.

$$2\left(b\ -\ 8\right)\ >\ 12$$  

• b > 20

• b > 6

• b > 14

• b > 20

Multiple Choice

Solve the inequality.

$$\frac{b}{2}<13$$  

• $$b<26$$  

• $$b\le26$$  

• $$b>26$$  

• $$b\ge26$$  

Multiple Choice

Solve the inequality.

$$6+2h>30$$  

• h < 24

• 18 > h

• h > 12

• h < -12

Multiple Choice

Solve the inequality.

7b - 3 < 11

• b < 2

• 84 > b

• b > 2

• b < 84

Open Ended

Give 1 possible solution for the inequality $$9x\ -32\ \ge13$$