Exercise 25 Page 396

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.

3/4 ≤ 1/2 +n

SubIneq

LHS-1/2≤RHS-1/2

3/4- 1/2 ≤ 1/2 +n- 1/2

▼

Simplify left-hand side

ExpandFrac

a/b=a * 2/b * 2

3/4-2/4 ≤ 1/2 +n-1/2

SubFrac

Subtract fractions

3-2/4 ≤ 1/2 +n-1/2

SubTerm

Subtract term

1/4 ≤ 1/2 +n-1/2

CommutativePropAdd

Commutative Property of Addition

1/4 ≤ 1/2-1/2 +n

DiffZero

1/2-1/2=0

1/4 ≤ n

RearrangeIneq

Rearrange inequality

n ≥ 1/4

Note that all values of n greater than or equal to 14 satisfy the inequality. Now let’s graph the inequality on a number line. Since n is greater than or equal to 14, we will shade to the right of our point at 14, including 14 with the closed circle.