Exercise 8 Page 394

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.

3/5 q ≤ 6

MultIneq

LHS* 5 ≤ RHS * 5

3/5 q* 5 ≤ 6* 5

CommutativePropMult

Commutative Property of Multiplication

3/5* 5 q ≤ 6* 5

NumberToDenomMultFrac

a = 5 * a/5

3 q ≤ 6* 5

Multiply

Multiply

3 q ≤ 30

DivIneq

.LHS /3.≤.RHS /3.

3q/3 ≤ 30/3

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Calculate quotient

MovePartNumRight

a* b/c=a/c* b

3/3q ≤ 30/3

QuotOne

a/a=1

1q ≤ 30/3

IdPropMult

Identity Property of Multiplication

q ≤ 10

We found that all values of q less than or equal to 10 will satisfy the inequality. Now let’s graph the inequality on a number line. Since q can equal 10, we draw a closed circle at this point. Since q is all values less than or equal to 10, we will shade the part of the number line that represents numbers less than or equal to 10. This means that we shade to the left of our point at 10, including 10 with the closed circle.