Unit 3 Solving and Creating Inequalities Unit Review

Unit 3 Solving and Creating Inequalities Unit Review

Lesson 3.1 Graphing and Writing Inequalities

• open dots are used in "greater than/less than"

• closed dots are used in "greater than or equal to" or "less than or equal to"

• arrow to the left is the lesser side

• arrow to the right is the greater side

Multiple Choice

Write the inequality represented by the graph

• $x>-10$

• $x<-10$

• $x\ge-10$

• $x\le-10$

Multiple Choice

Write inequality to represent the situation below.

"The cargo of the truck weighs more than 2000 pounds."

Use w to represent the weight (in pounds) of the cargo.

• $w>2000$
  

• $w<2000$

• $w\ge2000$

• $w\le2000$

Multiple Choice

Translate the sentence into an inequality.

A number x increased by 5 is less than -26

• $5x<-26$
  

• $x<-26$

• $x+5<-26$

• $x5<-26$

Lesson 3.2 Solving One-Step Inequalities

• Use inverse operation to solve

• watch out for the negative coefficient

Lesson 3.2 Solving One-Step Inequalities

1. Use inverse operation to solve
2. watch out for the negative coefficient

Multiple Select

For each value of x, determine whether it is a solution to  $x-28\ge12$  

• 42

• 45

• 36

• 40

Multiple Choice

 $-2x\ge18$  

Solve the inequality for x.

•  $x\ge20$  

•  $x\ge9$  

•  $x\le20$  

•  $x\le-9$  

Lesson 3.3 Solving and Creating Two-and Multi-Step Inequalities

• Solve just like an equation - using inverse operation & working backwards

• If you multiply or divide by a negative, remember to flip the inequality!

Multiple Select

 $-1+3v>-10$  

For each value of v, determine whether it is a solution to

• -3

• 6

• 8
  

• -4

Lesson 3.4 Solving Inequalities With Variables on Both Sides

• Move all variable terms to one side

Multiple Select

 $-5y-17>2y+11$  

Solve the inequality for y. Simplify your answer as much as possible.

• y<-4

• -4>y

• y=-4
  

• y>-4

• y>4

Lesson 3.5 Solving and Creating Compound Inequalities

• Compound Inequality: AND and OR

• Solving Compound Inequality

Multiple Select

Write the compound inequality show from the graph below.

• x<-2 or x>5

• x>5 or x<-2

• x=-2 and x=5

• x>5 and x<-2

• x>-2 and x<5

Multiple Choice

Solve the compound inequality.

 $3x-2>-5\ or\ 2x-1\le-11$  

•  $x<5\ and\ x\le-1$  

•  $x>-5\ or\ x\le-1$  

•  $x>-5\ and\ x\le5$  

•  $x>-1\ or\ x\le-5$  

Lesson 3.6 Solving Absolute Value Equations & Inequalities

• make sure the absolute value is greater than or equal to zero

• set the "inside" equal to both positive and negative number

• solve both equations/inequalities

• write your answer as x={a,b}

Multiple Choice

Solve. Use v={a, b} as your answer.

 $\left|v+7\right|=3$  

• v={4, 10}

• v={-10, -4}

• v={-3, -4}

• v={10, -4}

Multiple Select

Solve.

 $\left|5x-10\right|<5$  

• x<3 and x>1

• x>1and x<3

• x<1 or x<3

• x<3 or x<1

• x>3 and x>1