**Linear**

Inequalities

Inequalities

I'm at least 76.6" tall

I'm 4.5" less than Boomer

I'm 5" less than Carmello

I'm 2.5" taller than King

I'm 3.25" taller than Timmy

I'm at most 2.5" taller than Julie

Today I will:

Solve and graph linear inequalities.

What is an inequality?

An inequality is a relation between 2 expressions using <, >, <, and >.

How many solutions does an inequality have?

x > 5

There are infinite numbers greater than 5.

How do we show infinite solutions with an inequality?

x > 5

Can x = 5?

No, all values of x has to be bigger than 5.

How do we show this on a number line?

< or > open circle

< or > closed circle

How would we show this on coordinate plane?

x>5

Let's treat this like it is x = 5. How do graph it?

Because x can't equal 5, we will use a dashed line to represent at x=5.

x > 5

How do we show all the values greater than 5 on a graph?

Pick a point and test it to see if it is a solution.

Graph the inequality:

y < 5x - 1

STEPS:

1) Graph like it is y=5x-1

2) Because it can equal (<) we will use a solid line.

3) Pick a point and test it to see if it is part of the solution.

4) Shade everything on the side of the line that includes the point.

Name some points that are part of the solution.

(6, 0)

(7, 2)

(6.5, -10)

5) Notice, the points on the line ARE part of the solution.

Graph the inequality:

5x - 2y < 10

Graph using the intercepts.

We will use a dotted line.

Test a point. (0,0)

We will shade above the line.

How can we check to see if our shaded region is correct?

Pick a point in the shaded region and test to see if it is a solution.

(0, 4)

5x - 2y < 10

5(0) - 2(4) < 10

0 - 8 < 10

-8 < 10

(1,0)

y < 5x - 1

0 < 5(1) - 1

0 < 5 - 1

0 < 4

5(0) - 2(0) < 10

0 - 0 < 10

0 < 10

Assignment:

Graphing Inequalities

(0,0)

Because we only have x, that is all we can test.

0>5 is false. So,we will shade everything to the right.