Exercise 40 Page 190

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. For this exercise, distribute -2 on the left-hand side and -3 on the right-hand side, then simplify the terms to isolate t.

-2(0.5-4t)≥-3(4-3.5t)

Distr

Distribute (-2)

-1+8t≥-3(4-3.5t)

Distr

Distribute (-3)

-1+8t≥-12+10.5t

SubIneq

LHS-8t≥RHS-8t

-1≥-12+2.5t

AddIneq

LHS+12≥RHS+12

11≥ 2.5t

MultIneq

LHS* 2 ≥ RHS * 2

22≥5t

DivIneq

.LHS /5.≥.RHS /5.

22/5≥ t

RearrangeIneq

Rearrange inequality

t≤22/5

The solution to the inequality is t≤ 225.