# Lesson: Solve "and" inequalities

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### Lesson Objective

We will be able to solve and graph compound inequalities.

### Lesson Plan

Do Now: (5 minutes)

1) Write and graph an inequality for this statement:

All real numbers less than -5 and greater than or equal to -15.

2) Solve and graph:

3x – 5 > 2x + x – 7

3) 7 ½ ÷ 5

 Problem Solving: (20 minutes) Yesterday we learned that a compound inequality is the intersection of two graphs.  When we translated them from verbal to symbolic form we saw that they had two comparison signs.  Today we are going to focus on compound inequalities that have more than just a variable between the two comparison signs.   Solve 3x + 2 > 8. Explain steps for solving.  Make sure that whatever is done to one side of the inequality must be done to the other side is emphasized.   In our first example we had to subtract 2 from both sides of the inequality and divide both sides of the inequality by 8.  What do you think we would need to do to solve this inequality?   Ex. 11> 3x + 2 > 8   Solving compound inequalities works like a 3 sided inequality.  Whatever is done to one side must be done to the other two sides.   Ex. -14 < x – 8 < -1   Ex. -1 < -5t + 2 < 4

Guided Practice: (10 minutes)

Solve on white boards:

-7 > y – 8 > -12

-1 < -4m < 16

-6 <3n + 9 < 21

6 < x + 5 < 11

Assessment: (10 minutes)

Solving and graphing compound inequalities work-out

### Lesson Resources

 M6 4 3 work out   Assessment 193