Exercise 27 Page 396

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.

5/9v ≤ 45

MoveRightFacToNum

a/c* b = a* b/c

5v/9 ≤ 45

MultIneq

LHS* 9 ≤ RHS * 9

5v/9 * 9 ≤ 45* 9

FracMultDenomToNumber

a/9* 9 = a

5v ≤ 45* 9

Multiply

Multiply

5v ≤ 405

DivIneq

.LHS /5.≤.RHS /5.

5v/5 ≤ 405/5

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Calculate quotient

MovePartNumRight

a* b/c=a/c* b

5/5v≤ 405/5

QuotOne

a/a=1

1v≤ 405/5

IdPropMult

Identity Property of Multiplication

v≤ 405/5

CalcQuot

Calculate quotient

v ≤ 81

Note that all values of v less than or equal to 81 satisfy the inequality. Now let’s graph the inequality on a number line. Since v is all values less than or equal to 81, we will shade to the left of our point at 81, including 81 with the closed circle.