Solving Inequalities

The Solution of An Inequality is… Any value of the variable that makes the inequality true It is easier to understand the solution once it is graphed on a number line MUST be written as a complete mathematical sentence (x > 5 rather than just 5)

When solving inequalities… Use inverse operations Treat the inequality symbol the same as an equal sign.

When the problem is backwards -16 < x + 5 Move the –16 to the right and the x + 5 to the left Flip over the inequality symbol x + 5 > -16 Subtract 5 from both sides x + 5 – 5 > -16 – 5 x > -21

What happens when you multiply both sides of an inequality by a negative? -3 < 0 2 > -8 5 > 4 0 > -8

When multiplying or dividing both sides of an inequality by a negative You must flip the inequality symbol!!!

Example -3x > 15 Divide both sides by –3 Flip the inequality symbol

Example 2 Flip the inequality x > -128

Try these… x + 8 > -12 x – 12 < 17 x – 2 > -21

Try these…answers x + 8 > -12 x > -20 x – 12 < 17 x < 29 -21 -20 -19 28 29 30 -20 -19 -18 -31 -30 -29

Try these… 5x > -15 -14 < 7x -x > 3.4

Try these…answers 5x > -15 x > -3 -14 < 7x x > -2 -4 -3 -2 5x > -15 x > -3 -14 < 7x x > -2 -x > 3.4 x < -3.4 x < 2 x > -5/2 -3 -2 -1 -3.5 -3.4 -3.3 1 2 3 -3 -2 ½ -2