6.3 Compound Inequalities

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6.3 Compound Inequalities
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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 the teacher, the student has partial 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.
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Learn to Read

• alt x ltb
• Read x is between a and b
• alt x lt b
• Read x is between a b inclusive

4
Graph 1lt x lt 5
Read as ?
x is between 1 and 5
1
2
3
4
5
6
0
7
5
Write the inequality x greater than 2 or x less
than -1
x lt -1 x gt 2
Graph

-2
-1
0
1
2
3
Remember (closed circle) when the number is
included!
6
Solve Compound Inequalities and Graph
Solve like an equation, but now you have three
parts!
-9 lt 6x 3 39
Subtract 3 from all three parts.
-3
-3
-3
-12 lt 6x 36
Divide each part by 6.
6
6
6
-2 lt x 6
GRAPH
-2
-1
0
1
2
3
4
5
6 7
-3
7
Write the inequality, solve and then graph
Eight times a number x plus 4 is between -4 and
20.
-4lt 8x 4 lt 20
-4 -4 -4
-8 lt 8x lt 16
-1 lt x lt 2

-2
-1
0
1
2
3
8
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
x 4 gt 6 x gt 2 x 6 gt 4 x gt -2 length cannot
be negative 6 4 gt x 10 gt x
6
2 lt x lt 10
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Practice
Graph

1. x gt 4 and x lt -2 2. -2 lt x lt 3
-3 -2
-1
0
1
2
3 4 5

-2
-1
0
1
2
3

• Solve
• 2 x gt 3
• 3 lt 2 - x lt 5

x 3 -3 lt x lt -1
5. Write an inequality for the following graph
2 3 4 5 6 7 8 9 10
4 x 8