2.3 Solving Inequalities Using Multiplication and Division

Solving for the Variable Simplify Inequality (Distribute and/or combine like terms, if needed) Multiply or divide both sides of the equation by the coefficient to isolate the variable If you have to multiply or divide by a negative number to solve for the variable, then you must flip the inequality sign

Example 1 Solve the inequality 4x < 28, then graph the solution. 4 4 x < 7

Example 2 Solve -2y < 18 -2y < 18 -2 -2 y > -9

You try! a.) 2t < 56 t < 28 b.) -4x > 24 x < -6

Example 4 2 < y -3 -3 · 2 > y · -3 -6 > y or y < -6

You try! c) p < 7 -4 d) p > -28 3 < y or y > 3

Example 5 Solving Real Life Problems You earn $9.50 per hour at your summer job. Write and solve an inequality that you need to work to buy a digital camera that costs $247. hourly wage · hours worked > cost of camera 9.5h > 247 9.5 9.5 h > 26

You try! You have at most $3.65 to make copies. Each copy costs $.25. Write and solve an inequality that represents the number of copies you can make. .25c < 3.65 .25 .25 c < 14.6 (no such thing as .6 of a copy) c < 14