Exercise 6 Page 55

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(x-2)+4≥-3x+1

Distr

Distribute 3

x(3)-2(3)+4≥-3x+1

Multiply

Multiply

3x-6+4≥-3x+1

AddTerms

Add terms

3x-2≥-3x+1

AddIneq

LHS+3x≥RHS+3x

3x-2+3x≥-3x+1+3x

AddTerms

Add terms

6x-2≥1

AddIneq

LHS+2≥RHS+2

6x≥3

DivIneq

.LHS /6.≥.RHS /6.

6x/6≥3/6

CalcQuot

Calculate quotient

x≥3/6

ReduceFrac

a/b=.a /3./.b /3.

x≥1/2

This inequality tells us that all values greater than or equal to 12 will satisfy the inequality. Therefore, answer G is correct.