5.1/5.2 Solving Inequalities

5.1/5.2 Solve Inequalities

EQ: How do you know when to flip the sign for an inequality?

You have 20 min to do a 4 questions quiz. You can use your notes

After the quiz Get your computers and notes out, write title and EQ and we will go through the Quizziz lesson.

Your HW last class was IXL, so you have nothing to turn in today

What is an inequality?

Inequality - Compares two values, showing if one is less than, greater than, less then OR equal to or greater then or equal to another value.

17 > 12 17 is greater than 12

5 < 23 5 is less than 23

With your partner, try and answer.

1.y < -3

a.-3

b.7

c.-9

d.10

e.-4

2.m ≥ 1

a.-1

b.1

c.-8

d.3

e.5

Directions: Select ALL answers that could be a value for the variable

3.8 < p

a.11

b.10

c.1

d.-4

e.8

4.k ≤ 4

a.0

b.-12

c.4

d.9

e.-4

5.b ≥ 0

a.-5

b.-3

c.0

d.3

e.4

6.-10 ≤ w

a.-11

b.3

c.6

d.0

e.-5

Graphing Inequalities

Open Circle

Less than <
Greater than >

Closed Circle

Less than or equal to ≤
Greater than or equal to (≥)

Greater than

Greater than or equal to

Less than

Less than or equal to

When graphing inequalities you need to look at two things:
1. Open or Closed Circle
2. Direction of the arrow

**The direction of the arrow shows all the possible outcomes for the variable**

Multiple Choice

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

• ≤, ≥ 
• <, >

Multiple Choice

Pick the correct letter for:

6 > x

• A

• B

• C

• D

Multiple Choice

What inequality does the number line graph represent. 

• x < 2
• x > 2
• x ≥ 2
• x ≤ 2

Multiple Choice

Pick the correct inequality.

• A
• B
• C
• D

Multiple Choice

Select the inequality shown

• x > 5

• x ≥ 5

• x < 5

• x ≤ 5

Multiple Choice

Select the inequality shown

• x > 1

• x ≥ 1

• x < 1

• x ≤ 1

Multiple Choice

Which graph matches the inequality
2 > p?

• A
• B
• C
• D

Ex: Solving One-Step Inequalities

When solving inequalities, you solve the same way we did for solving algebraic equations.

1.

3y > 15

2. 24 ≥ x - 14

The only difference is when you MULTIPLY or DIVIDE
BOTH sides by a negative the sign flips

Should we flip the sign? YES or NO.

1.

3y > 18 __________

3. 18 > -p __________

2.

-9n < 27 __________

4. h/-6 ≥ -18 __________

5.

7. -20 ≤ -3p + 4

Multiple Choice

Solve the inequality.
x + 5 ≤ 13

• x ≥ 8
• x ≥ 18
• x ≤ 8 
• x ≤ 18 

Multiple Choice

Does the sign need to flip when solving?

-2x ≥ 22

• YES

• NO

Multiple Choice

Which is the solution of 
-6a ≥ -36

• a ≥ 6
• -6 ≥ a
• a ≤ 6
• 6 ≤ a

Multiple Choice

Solve the following inequality:

x - 14 > 10

• x > 24

• x < 24

• x > -4

• x < -4

Multiple Choice

What is the first step to solve this equation? 3x - 5 = 7

• Add 5 to both sides of the equation

• Add 3x to both sides of the equation

• Subtract 5 from both sides of the equation

• Subtract 7 from both sides of the equation

Multiple Choice

Review Chapter 1

Solve for w

• w = 2

• w = 4

• w = 6

• w = 8

Ex: Solving Multi-Step Inequalities

When solving inequalities, you solve the same way we did for solving algebraic equations.

1.

2 + 5x > 57

2. -7 - 2n ≤ 5

Multiple Choice

Solve the following Inequality:

2x + 4 > 24

• x > 4

• x > 10

• x < 10

• x > 14

Multiple Choice

2x - 3 + 4x = 27

• 12
• 4
• 5
• 15

Multiple Choice

Solve: 18 = 3(x - 2)

• 6.7
• 4
• 8
• -4

Inequalities!

Multiple Choice

Solve. Check your solution.

$$3<4\left(x+2\right)$$  

• $$x>-1.25$$  

• $$x<-1.25$$  

• $$x>1.25$$  

• $$x<1.25$$  

Multiple Choice

Which graph matches the inequality
r ≥ -6?

• A
• B
• C
• D

Multiple Choice

Solve. Check your solution.

$$4\left(b-3\right)\le72$$  

• $$b\ge21$$  

• $$b\le60$$  

• $$b\le21$$  

• $$b\le15$$  

Multiple Choice

What is the first step in solving a multi-step equation?

• Distribution (If necessary)

• Combine Like Terms

• Move the variable

• Move the constant

Multiple Choice

You flip an inequality symbol when you...

• subtract
• multiply and divide only
• multiple by a negative number
• multiple or divide by a negative number

Multiple Choice

-4x + 14 ≤ 54

• x ≥ -10
• x ≤ -10
• x ≥ 10
• x ≤ 10

5.1/5.2 Homework

Pg. 267 #2-18 EVEN (9problems)
Pg 268 #22-36 EVEN (8problems)
Pg 274 #16-20 EVEN (3problems)

20 Total Problems