Exercise 49 Page 398

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. 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

▼

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.