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Big Ideas Math: Modeling Real Life, Grade 6
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Big Ideas Math: Modeling Real Life, Grade 6 View details
8. Solving Inequalities
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Exercise 28 Page 396

What can you do to isolate a variable in an inequality?

Solution: x ≥ 48
Graph:

Practice makes perfect

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when we divide or multiply by a negative number, we must reverse the inequality sign.

5x/8 ≥ 30
MultIneq

LHS* 8 ≥ RHS * 8

5x/8 * 8 ≥ 30 * 8
FracMultDenomToNumber

a/8* 8 = a

5x ≥ 30* 8
Multiply

Multiply

5x ≥ 240
DivIneq

.LHS /5.≥.RHS /5.

5x/5 ≥ 240/5
â–¼
Calculate quotient
MovePartNumRight

a* b/c=a/c* b

5/5x≥ 240/5
QuotOne

a/a=1

1x≥ 240/5
IdPropMult

Identity Property of Multiplication

x≥ 240/5
CalcQuot

Calculate quotient

x ≥ 48

Note that all values of x greater than or equal to 48 satisfy the inequality. Now let’s graph the inequality on a number line. Since x is all values greater than or equal to 48, we will shade to the right of our point at 48, including 48 with the closed circle.

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arrow_right Try It p.392-394
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Try It 2 (Page 392)
Try It 3 (Page 392)
Try It 4 (Page 393)
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Try It 6 (Page 393)
Try It 7 (Page 394)
Try It 8 (Page 394)
Try It 9 (Page 394)
arrow_right Self-Assessment for Concepts & Skills p.394
Self-Assessment for Concepts & Skills 10 (Page 394)
Self-Assessment for Concepts & Skills 11 (Page 394)
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arrow_right Self-Assessment for Problem Solving p.395
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arrow_right Review & Refresh p.396
Review & Refresh 1 (Page 396)
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Review & Refresh 10 (Page 396)
arrow_right Concepts, Skills, & Problem Solving p.396-398
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