6.3 Compound Inequalities

Learning Goal for Focus 2(HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3):

The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step.

4 3 2 1 0

In addition to level 3.0 and above and beyond what was taught in class,  the student may:- Make connection with other concepts in math- Make connection with other content areas.

The student will create equations from multiple representations and solve linear equations and inequalities in one variable explaining the logic in each step. - rearrange formulas to highlight a quantity of interest.-Graph created equations on a coordinate graph.

The student will be able to solve linear equations and inequalities in one variable and explain the logic in each step.-Use equations and inequalities in one variable to solve problems.

With help from theteacher, the student haspartial success with solving linear equations and inequalities in one variable.

Even with help, the student has no success with solving linear equations and inequalities in one variable.

Learn to Read…a< x <b

Read: x is between a and b

a< x < b Read: x is between a & b inclusive

Graph: 1< x < 5

Read as: ?

1 2 3 4 5 60 7

x is between 1 and 5

Write the inequality x greater than 2 or x less than -1

x < -1 x > 2

Graph:

-2 -1 0 1 2 3

*Remember:

(closed circle) • when the number is included!

Solve Compound Inequalities and Graph:

-9 < 6x + 3 ≤ 39

Solve like an equation, but now you have three parts!

-3 -3 -3

-12 < 6x ≤ 36

Subtract 3 from all three parts.

Divide each part by 6.6 6 6

-2 < x ≤ 6

GRAPH:-2 -1 0 1 2 3 4 5 6 7-3

Eight times a number x plus 4 is between -4 and 20.

Write the inequality, solve and then graph:

-4< 8x + 4 < 20-4 -4 -4-8 < 8x < 16-1 < x < 2

-2 -1 0 1 2 3

Use inequalities to solve the following problem.

What are the restriction on the value of x in the triangle? Remember that two side of a triangle must add up to be greater than the third side.

You must set up three inequalities!x 4

6

x + 4 > 6 x > 2

x + 6 > 4 x > -2 *length cannot be negative*

6 + 4 > x 10 > x

2 < x < 10

Practice:

1. x > 4 and x < -2

2. -2 < x < 3

Graph

Solve

3. 2 + x > 3

4. 3 < 2 - x < 5

1

3

5. Write an inequality for the following graph

2 3 4 5 6 7 8 9 10

-3 -2 -1 0 1 2 3 4 5

-2 -1 0 1 2 3

x ≥ 3

-3 < x < -1

4≤ x ≤ 8