7EE4b

Solving Inequalities

MGSE7.EE.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem

To graph x > 5, draw an open circle at 5 on a number line.

• It is an open circle because <, > get open circles.

• ≤, ≥ get closed circles.

Find several solutions and color those on a number line.

7 and 9 are solutions because 7 > 5 and 9 > 5.

Start at the open circle and color over the solutions you found. Draw an arrow to show that the solutions go on forever.

Multiple Choice

more than

• <

• >

• ≤

• ≥

Multiple Choice

At Least

• <
• >
• ≤
• ≥

Multiple Choice

No More Than

• <
• >
• ≤
• ≥

Multiple Choice

less than or equal to

• <
• >
• ≤
• ≥

Multiple Choice

- 2k > 18

• k is greater than 20
• k is less than negative 9
• k is greater than negative 9
• k is less than 36 

Multiple Choice

8x ≥ -32

• x ≥ -4
• x ≥ 4
• x ≤ -4
• x ≥ 4

Multiple Choice

Pick the correct letter for:
6 > x

• A
• B
• C
• D

Multiple Choice

x + 5 > 7

• x > -2

• x > 2

• x > 12

• x > -12

Multiple Choice

Match the graph with its inequality.

• 11 < a
• 11 > a
•  11 ≤ a
•  11 ≥ a

Multiple Choice

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

• <, >
• ≤, ≥ 
• ≤, <
• ≥, >

Multiple Choice

Solve the inequality.
x + 5 ≤ 13

• x ≥ 8
• x ≥ 18
• x ≤ 8 
• x ≤ 18 

Multiple Choice

-20>18+m

• M<-38
• M<38
• M>38

Draw

Find the solution set to

$$x\ +\ 4\ \le\ 7$$

Express in set notation and on the number line

Multiple Choice

Solve the inequality.

• k ≤ –11
• k ≤ –5
• k ≤ 8
• k ≤ –3

Multiple Choice

Do I need to flip my sign?
-3x  ≥ 12

• Yes

• No

Multiple Choice

Solve the inequality

-5x - 7 < -28

• x > -7

• x < -7

• $$x\ >\ \frac{21}{5}$$

• $$x\ <\ -\frac{21}{5}$$

Multiple Choice

7b - 3 < 11

• b < 2
• 84 > b
• b > 2
• b < 84

Multiple Choice

4x - 10 ≤ 22

• x ≤ 8
• x ≥ 8
• x ≤ 3
• x ≥ 3

Multiple Choice

15 + 7x ≥ 29

• x ≥ 2
• x ≥ -2
• x ≤ 2
• x > 2

Multiple Choice

What are two solutions to
x < 8?

• 8.6, 7.9
• 11, 16
• 0.8, 5.9
• 12, 7.1

Multiple Choice

-9x + 7 ≥ 25

• x ≥ -3.6
• x ≤ 2
• x ≥ -2
• x ≤ -2

Open Ended

Name three solutions for h > 8.

Open Ended

Name three solutions for z ≤ 11.

Audio Response

Find the solution to the

$$6\left(x\ -\ 5\right)\ \ge\ 30$$

Explain how you found the solution and where to graph on the number line.

Open Audio Recorder

Solving Multi-step inequalities

• very similar to solving multi-step equations

• combine like terms

• get all the variables on one side
  

• isolate the variables
  
  

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

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

Multiple Choice

Solve the inequality.

2(b - 8 ) > 12

• b > 20

• b > 6

• b > 14

• b < 20

Fill in the Blank

$$4\left(4n-3\right)\le\left(-44\right)$$   The first thing I need to do is distribute the ___ to 4n and 3.

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

Now solve  $$16n-12\le-44$$  

• $$n\ge-2$$  

• $$n\le-2$$  

• $$n\ge2$$  

Multiple Choice

$$3\left(3+3n\right)>27$$  

• $$n>2$$  

• $$n<2$$  

• $$n\ge3$$  

Something interesting happens when you multiply or divide both side of an inequality by a negative number.

Open Ended

Take for example....

$$3>1$$  We know this is true. 3 is greater than 1. But what if we multiplied both sides by -1.... $$\left(-1\right)3>\left(-1\right)1$$  Then we get this.... $$-3>-1$$  THIS ISN'T TRUE!!! The only way to make it true would be to flip around the inequality like this.. $$-3<-1$$  

Multiple Choice

Solve this...... $$3\left(3-3n\right)<36$$  

• $$n<-3$$  

• $$n>-3$$  

• $$n\le-3$$  

Multiple Choice

Now lets put it all together! Distribute, combine and solve!! $$-3\left(2-3x\right)<-33$$  

• $$x<3$$  

• $$x>-3$$  

• $$x<-3$$  

Draw

Find the solution set to

$$8y\ +\ 4\ <\ 7y\ -\ 2$$

Express the solution in set notation and on a number line.

Draw

Find the solution to

$$-\frac{x}{12}\le\frac{1}{4}$$

Express the solution in set notation and on the number line.

Draw

Find the solution to

$$-3\left(2x\ +\ 4\ \right)\ >\ 0$$

Express the solution in set notation and on the number line.

Poll

How do you feel about solving inequalities now?

• Great

• Good

• Ok

• Not good