Download 3.4 Solving Two-Step and Multi

3.4 Solving Two-Step and Multi-Step Inequalities
Algebra 4.0, 5.0
Solve inequalities that contain more than one operation.
Main Idea
• When we solve multi-step equations:
– We use more than one operation
– We use inverse operations
– We may need to combine like terms
– We may need to use the distributive property
– We may need to multiply reciprocals to get rid of
fractions
• All these items hold true for inequalities
• What do we need to be careful of?
Two-Step Inequalities: Practice
1) -12 > 3x + 6
x
3)
53
2
2) 8 – 3y > 29
x
4 )  4  4
3
Example-Solving Multi-Step
Inequalities
• Solve and graph solution
Example: Distributive Property
Solve the inequality and graph the solutions.
–4(2 – x) ≤ 8
−4(2 – x) ≤ 8
−4(2) − 4(−x) ≤
8
–8 + 4x ≤ 8
+8
+8
4x ≤ 16
Distribute –4 on the left side.
Since –8 is added to 4x, add 8 to
both sides.
Since x is multiplied by 4, divide
both sides by 4 to undo the
multiplication.
The solution set is {x:x ≤ 4}.
x≤4
–10 –8 –6 –4 –2
0
2
4
6
8 10
Example: Distributive Property & Combine Like Terms
Solve the inequality and graph the solutions.
Check your answer.
3 + 2(x + 4) > 3
Distribute 2 on the left side.
3 + 2(x + 4) > 3
3 + 2x + 8 > 3
2x + 11 > 3
– 11 – 11
2x
Combine like terms.
Since 11 is added to 2x, subtract
11 from both sides to undo the
addition.
Since x is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
The solution set is {x:x > –4}.
> –8
x > –4
–10 –8 –6 –4 –2
0
2
4
6
8 10
Multi-Step Practice
• Solve and graph solution.
Example-Simplify before Solving
• Solve and graph solutions
Example-Simplify before Solving
• Solve and graph solutions
Example-Simplify before Solving
• Solve and graph solutions
Practice
• Solve and graph solutions
Review
1) What is important to remember when
solving inequalities?
2) What is difficult when solving multi-step
inequalities?