1. Objective
3.6 solve multi-step inequalities

2. Warm-up Solve Multi-Step Equations
Remember this?
Warm-up Solve Multi-Step Equations
In your notebook, complete the following three examples. Show all of your steps.

3. Section 3.6 “Solve Multi-Step Inequalities”
The steps for solving two-step and multi-step
equations can be applied to linear inequalities.
Solving Multi-Step Inequalities
STEP 1- Use distributive property and combine like terms.
STEP 2- Collect variables on one side of the equation.
STEP 3- “Undo” addition and/or subtraction.
STEP 4- “Undo” multiplication and/or division. (If multiplying or dividing by a negative, flip the inequality sign).
STEP 5- Solve for the variable.
STEP 6- Check your work.
STEP 7- Graph your solution

4. REMEMBER!!!!!
Multiplying and/or dividing each side of an inequality by a NEGATIVE number only produces an equivalent inequality IF the inequality sign is REVERSED!!

5. Solving Two-Step Inequalities…
Isolate the variable! Get ‘x’ by itself.
3x + 5 > -19
To get the ‘x’ by
itself first get rid
of “adding 5.” 5 5
Do the opposite.
“Subtract 5.”
Whatever you do to
one side of the inequality
you must do the other side.
3x > -24
To get the ‘x’ by
itself get rid
of “multiplying by 3.” 3 3
Do the opposite.
“Divide by 3.”
x > -8

6. 3x – 7 < 8. Graph your solution. Solve
Write original inequality.
3x < 15
Add 7 to each side.
x < 5
Divide each side by 3.
ANSWER
The solutions are all real numbers less than 5. Check by substituting a number less than 5 in the original inequality.

7. Solve – 6(x – 5) ≤ 150 –6(x – 5) ≤ 150 –6x + 30 ≤ 150 - 30 - 30
Write original inequality.
–6x ≤ 150
Distributive property
– 6x ≤ 120
Subtract 30 from each side. –
x >
–20
Divide each side by Reverse
inequality symbol. –
ANSWER
The solutions are all real numbers greater than equal Check by substituting a number more than -20 in the original inequality.

8. 6x – 7 > 2x+17. Graph your solution. Solve
Subtract 2x from each side.
-2x x
4x – 7 > 17
Add 7 to each side.
4x > 24
Divide each side by 4.
x > 6
ANSWER
The solutions are all real numbers greater than 6.

9. Practice