Exercise 9 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.

5 > 5t/6

MultIneq

LHS* 6 > RHS * 6

5 * 6> 5t/6* 6

Multiply

Multiply

30 > 5t/6* 6

FracMultDenomToNumber

a/6* 6 = a

30 > 5t

DivIneq

.LHS /5.>.RHS /5.

30/5 > 5t/5

RearrangeIneq

Rearrange inequality

5t/5 < 30/5

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Calculate quotient

MovePartNumRight

a* b/c=a/c* b

5/5t < 30/5

QuotOne

a/a=1

1t < 30/5

IdPropMult

Identity Property of Multiplication

t < 30/5

CalcQuot

Calculate quotient

t < 6

We found that all values of t less than 6 will satisfy the inequality. Now let’s graph the inequality on a number line. Since t cannot equal 6, we draw an open circle at this point. Since t is all values less than 6, we will shade the part of the number line that represents numbers less than 6. This means that we shade to the left of our point at 6.