Solving Inequalities Solving inequalities follows the same procedures

Solving Inequalities ● Solving inequalities follows the same procedures as solving equations. ● There a few special things to consider with inequalities: ● We need to look carefully at the inequality sign. ● We also need to graph the solution set.

Review of Inequality Signs > greater than < less than greater than or equal less than or equal

How to graph the solutions > Graph any number greater than. . . open circle, line to the right < Graph any number less than. . . open circle, line to the left Graph any number greater than or equal to. . . closed circle, line to the right Graph any number less than or equal to. . . closed circle, line to the left

Solve the inequality: x+4<7 -4 -4 x < 3 ●Subtract 4 from each side. ●Keep the same inequality sign. ●Graph the solution. • Open circle, line to the left. 0 3

Can we always undo and keep the inequality true? n n n Let’s investigate: 2 < 6 Adding to both sides? 2+2<6+2 Subtracting on both sides? 2– 2<6 -2

Can we always undo and keep the inequality true? n n n Let’s investigate: 2 < 6 Multiply both sides? 2∙ 2<6∙ 2 Dividing on both sides? 2 2<6 2

So far so good? n n n What about multiplying and dividing by a negative number? : 2 < 6 Multiply both sides by -2? 2 ∙ -2 < 6 ∙ -2 If we multiply or divide by a negative number we need to flip the inequality sign.

There is one special case. ● You only reverse the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Example: Solve: -3 y + 5 >23 ●Subtract 5 from each side. -5 -5 -3 y > 18 -3 -3 ●Divide each side by negative 3. y < -6 ●Reverse the inequality sign. ●Graph the solution. • Open circle, line to the left. -6 0

Try these: ● Solve 2 x+3>x+5 ● Solve - x - 11>23 ● Solve

Homework: