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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 49 Page 398

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

Solution: b ≤ 6
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.

2 25b-1 310b ≤ 6 35
MixedToFrac

a bc=a* c+b/c

2* 5+2/5b-1*10+3/10b ≤ 6*5+3/5
â–¼
Simplify left-hand side
SimpQuot

Simplify quotient

12/5b - 13/10b ≤ 33/5
ExpandFrac

a/b=a * 2/b * 2

12* 2/5* 2b - 13/10b ≤ 33/5
Multiply

Multiply

24/10b-13/10b ≤ 33/5
SubFrac

Subtract fractions

24-13/10b ≤ 33/5
SubTerm

Subtract term

11/10b ≤ 33/5

Next, we will use the Multiplication Property of Inequality to simplify the inequality even further.

11/10b ≤ 33/5
MultIneq

LHS* 10 ≤ RHS * 10

10 * 11/10b ≤ 10 * 33/5
DenomMultFracToNumber

10 * a/10= a

11b ≤ 10* 33/5
MoveLeftFacToNum

a*b/c= a* b/c

11b ≤ 10* 33/5
Multiply

Multiply

11b ≤ 330/5
CalcQuot

Calculate quotient

11b≤ 66

Finally, let's use the Division Property of Inequality to simplify the inequality.

11b≤ 66
DivIneq

.LHS /11.≤.RHS /11.

11b/11 ≤ 66/11
â–¼
Calculate quotient
MovePartNumRight

a* b/c=a/c* b

11/11b≤ 66/11
QuotOne

a/a=1

1b≤ 66/11
IdPropMult

Identity Property of Multiplication

b≤ 66/11
CalcQuot

Calculate quotient

b ≤ 6

Note that all values of b less than or equal to 6 satisfy the inequality. Now let’s graph the inequality on a number line. Since b is all values less than or equal to 6, we will shade to the left of our point at 6, including 6 with the closed circle.

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arrow_right Try It p.392-394
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Try It 2 (Page 392)
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arrow_right Self-Assessment for Concepts & Skills p.394
Self-Assessment for Concepts & Skills 10 (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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arrow_right Concepts, Skills, & Problem Solving p.396-398
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