Solving Inequalities

Pages 142 - 144

Solving Inequalities●Solving inequalities follows the same procedures as solving equations.

●There are 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< 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.

30

<

There is one special case.

●Sometimes you may have to reverse the direction of the inequality sign!!

●That only happens when you

multiply or divide both sides of the inequality by a negative number.

Solving an Inequality

Solve 5 + y <13

5 + y < 13

Subtract 5 to each side.

Write original inequality.

Simplify.

5 + y - 5 < 13 - 5

y < 8

To graph y < 8, use an open dot and draw the arrow pointing to the left.

73 4 5 6 982 10

Then graph the solution.

Example 1:

Solving an Inequality

Solve a – 3 > -5

a – 3 > -5

Add 3 to each side..

Write original inequality.

Simplify.

a – 3 + 3 > -5 + 3

a > -2

To graph a > -2 use a closed dot and draw the arrow pointing to the right.

Then graph the solution.

2–2 –1 0 1 43–3 5

Example 2:

Solve: -3y + 5 >23

-5 -5

-3y > 18

-3 -3

y < -6

●Subtract 5 from each side.

●Divide each side by negative 3.

●Reverse the inequality sign.

●Graph the solution.

• Open circle, line to the left.

0-6

Example 3:

Solving Inequalities

Solving Inequalities

Try these:

●Solve 2x+3>x+5

●Solve - c - 11>23

●Solve 3(r-2)<2r+4