Exercise 65 Page 192

We can solve inequalities in almost the same way as equations. The only difference is that we need to remember to flip the inequality sign when multiplying or dividing by a negative value.

-t/3≤1

MoveNegFracToDenom

Put minus sign in denominator

t/-3≤1

MultNegIneq

Multiply by -3 and flip inequality sign

t≥-3

This inequality tells us that all values greater than or equal to -3 will satisfy the inequality.

Checking Our Answer

Checking Our Answer

To check our answer, let's use the given inequality to test a few values in a table.

t	-t/3≤1	Simplify	True or False?
-6	-( -6)/3? ≤1	2≰1	False
-3	-( -3)/3? ≤1	1≤1	True
0	-( 0)/3? ≤1	0≤1	True

Notice how the values greater than or equal to - 3 make the inequality true.