Example 2

Example 3

Practice Time! Try Both Kinds!

**6.2 Solving Inequalities**

**Solving Inequalities**

WHAT

: Solving inequalities for the unknown variable

Keypoints

Solving inequalities is the

same as

solving

equations

except...

Example 1

Your turn! :]

Try to solve these problems and graph your answer.

Two Step Inequalities!

Because you know how to solve equations, this will just take practice! *Remember to flip the sign when multiplying or dividing by a negative number.

Multi-Step Equations

Alright, AGAIN! You've seen these problems before! Just do what you do best, and remember the rules regarding the inequality symbol! :)

HOW

: Isolate the variable to one side of the inequality using inverse operations

ONE DIFFERENCE

:

When multiplying or dividing by a negative number, switch the direction of the sign/inequality symbol

Examples ahead!

**This should be easy enough!**

**It's just like solving equations! :]**

Adding and Subtracting- One Step Equations

Example 1:

17 + k 10

subtract 17 on both sides

17 + k 10

-17

-17

k -7

Graph:

k -7

k is less than or equal to (filled in circle)

less than = arrow to the left

Check your answers!

x - 1

3

add one on both sides

x - 1

3

+1

+1

x 4

-18 + n < -7

add 18 on both sides

-18 + n < -7

+18

+18

n < 11

*

Remember

: When multiplying or dividing by a

negative

number,

flip the sign

.

17. 24 -4n

divide by -4 on each side

-4

-4

divided by negative

switch the sign

-6

n

-6

n

or n

-6

Now your turn!

Solve and graph

Did you get the right answer? Check here!

m

5

3

multiply by 3 on both sides

m

15

multiplied by positive number

sign stays the same

Check Your Answers! :)

n > -13

p

3

k -7

*Try NOT flipping the sign to see why we must!

-11 x - 4 > -15

step 1: add 4 on both sides

+4

+4

-11x > -11

step 2: divide by -11 on both sides

-11

-11

*since I divided by a negative, switch the sign

x >

-1

x

<

-1

*open circle

*less than- to the left

Your Turn! Practice Problems. :]

SHOW YOUR WORK!

#9. 1. subtract 5 on both sides

2. Divide by -7 on both sides

3. Switch the sign (divided by a negative) and graph

1. Multiply by 2 on both sides

2. Subtract by 3 on both sides

1. Multiply by 2 on both sides

2. Subtract 1 on both sides

#12. 1. Add 2 on both sides

2. Times by 2 on both sides

Multi-step:

1. Use the distributive property.

1. -3p - (-21)

21

2. Add the opposite (leave, change, change)

2. -3p + (+21)

21

3. -3p + 21

21

3. Subtract 21 from each side.

-21

-21

-3p

0

4. Divide by -3 on both sides/ change the direction of the sign.

p

0

check your answer and graph!

Multi-step Inequalities Practice Problems

Try them on your own!

Make sure to show your work!

Answers and Steps

1. Combine like terms on both sides of the inequality

-6x - 16 < 2x

2. Bring all x terms to one side- Add 6x on both sides

- 16 < 8x

3. Divide each side by 8

-2 < x or x > -2

1. Combine like term on both sides.

-7 -6x > -11 -7x

2. Bring all x terms to one side-

Add 7 x to both sides

-7 + x > - 11

3. Add 7 to both sides

x > -4

#10.

#11.