Solve multi-step inequalities

Solving Multi-Step Inequalities

Solving Multi-step inequalities

• very similar to solving multi-step equations

• combine like terms

• get all the variables on one side
  

• isolate the variables
  
  

Solving Inequalities is like Solving Equations

• Distribute First

• Get Like Terms together

• Do Opposite Operations

• BUT... If you divide or multiply by a NEGATIVE NUMBER you must flip the inequalitiy sign

Multiple Choice

Does the sign need to flip when solving?

m - 5 > 8

• YES

• NO

Multiple Choice

Does the sign need to flip when solving?
-2x ≥ 22

• YES
• NO

Multiple Choice

Solve this

$$3x+4\le19$$  

• x = 5

•   $$x\ >5$$  

• $$x\le5$$  

Multiple Choice

Solve for t.

6t + 4 ≤ -2

• t ≤ -1 
• t ≤ 1
• t=1
• 1=t

Multiple Choice

Solve
-5m < 10

• m < -2
• m > -2
• m < -50
• m > -50

Multiple Choice

Now solve 

$$16n-12\le-44$$  

• $$n\ge-2$$  

• $$n\le-2$$  

• $$n\ge2$$  

Sometimes you have to combine like terms before you can solve the inequality

Multiple Choice

$$8n-6n>24$$

 What is your first step in solving this inequality?

• Subtract 8n on both sides

• Combine 8n and -6n

• Add 6n on both sides

Multiple Choice

What is the answer to this inequality?

8n-6n>24

• 
  

  $$n>12$$

• $$n<12$$

• $$n\ge12$$

Multiple Choice

-4x + 9 - x < -3

• x > 2.4

• x < 2.4

• x > -2.4

• x < -2.4

Multiple Choice

6x + 2 + 6x < 14

• x < 1
• x > 1
• x < -1
• x > -1

Sometimes you must distribute first, and then combine like terms before you can solve the inequality. 

Multiple Choice

$$3\left(3+3n\right)>27$$  

• $$n>2$$  

• $$n<2$$  

• $$n\ge3$$  

Multiple Select

$$4\left(4n-3\right)\le\left(-44\right)$$  

After distributing, my iniquality should look like what?

• $$8n-3\le-44$$  

• $$8n-7\le-44$$  

• $$16n-12\le-44$$  

• $$16n-3\le-44$$  

Multiple Choice

Solve the inequality

• x ≥ -7

• x ≤ -7

• x ≤ -15

• x ≥ -15

Multiple Choice

-2(5 + 6n) < 6(8 − 2n)

• no solution
• infinite solution
• x < 0
• x > 0

Graphing Inequalities: Remember your open dots (< and >) and your closed dots!

Also keep in mind you want to keep the LETTER ON THE LEFT so your arrow points the correct way.

Multiple Choice

Match the graph with its inequality.

• b > –2
• b < –2
• b ≥ –2
• b ≤ –2

Multiple Choice

Match the graph with its inequality.

• c > 9
• c < 9
• c ≥ 9
• c ≤ 9

Multiple Choice

Match the graph with its inequality.

• a > 11

• a < 11

• a ≥ 11

• a ≤ 11

Multiple Choice

Which sentence represents m > 41?

• Mary’s points, m, totaled more than 41
• Calvin ran no less than 41 miles, m
• The temperature, m, was less than 41°F
• The magazines’ cost, m, was not more than $41.

Multiple Choice

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

• <, >
• ≤, ≥ 
• ≤, <
• ≥, >

Multiple Choice

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

• ≤, ≥ 
• <, >
• ≤, <
• ≥, >

Multiple Choice

"At most" and "No more than" are both clue words for...

• <
• >
• ≤
• ≥

Multiple Choice

Distribute, combine and solve!!

$$-3\left(2-3x\right)<-33$$  

• $$x<3$$  

• $$x>-3$$  

• $$x<-3$$  

Multiple Choice

$$33\le3\left(2+3p\right)$$  

• $$p<3$$  

• $$p<11$$  

• $$p\ge3$$  

Multiple Choice

Your taxi fare is $2.50 per mile, plus a $5 fee.  You cannot exceed $20.  Which inequality models this scenario?

• 5x + 2.50 ≤ 20
• 2.50x + 5 < 20
• 2.50x + 5 ≤ 20
• 7.50x < 20