Exercise 4 Page 298

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. We will start by using the Distributive Property and combining like terms.

2(n + 3) - 4< 6

Distr

Distribute 2

2n + 6 - 4 < 6

SubTerm

Subtract term

2n + 2 < 6

SubIneq

LHS-2

2n < 4

DivIneq

.LHS /2.<.RHS /2.

2n/2< 4/2

CalcQuot

Calculate quotient

n < 2

The above tells us that all values of n that are less than 2 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that n can not equal 2, which we show with an open circle on the number line.