Lesson: Graph compound inequalities

Do Now: (5 minutes)

1) Solve and graph:

2x + 1 – 4x > 8 - 6x – 10

2) Write an inequality from the following description:

All numbers that are less than -5.

3) Solve for x: (x - 2) / 3 = 5

Problem Solving: (15 minutes)

Last week we learned how to graph one-step and multi-step inequalities.  Today we are going to take it a step further by graphing compound inequalities.  Compound inequalities are broken into two types- “and” and “or”.  We are going to work with “and” inequalities today.

“And” inequalities are useful when you are describing something that fits between a range of numbers.  Highway speed limits are a great example of this.  There is a maximum speed that you can’t go higher than and there is also a minimum speed that you can’t go lower than.

Ex. The maximum speed on a highway is 65 mph. The minimum speed is 45 mph.  Represent this as a compound inequality.

Our simple inequalities had lines that continue forever.  For compound inequalities, only include the part of the number line that has both lines as the solution.

The graph of a compound inequality and is the intersection of the graphs of the inequalities.

Ex.  x > -2

        x< 1

x> -2 and x< 1

-2 < x < 1

Compound inequalities with “and” can be written with the x in the middle.

Ex.  All real numbers that are less than 6 and greater than 2.

Ex. -6 < x < 3

Guided Practice: (5 minutes)

All real numbers that are less than 6 and greater than 2.

All real numbers that are greater than -8 and less than or equal to 20.

Assessment: (5 minutes)

Compound inequalities work-out