1.6 Solving Linear Inequalities Algebra II

Steps for Solving Multi-Step Inequalities 1.) Simplify (use distributive prop., add like terms, or multiply by the denominator) 2.)When the variable is on both sides of the Inequality, then add the opposite of either one to both sides. 3.) Add the opposite of the number on the same side of the variable to both sides.

Steps (continued) 4.) Divide by the coefficient OR multiply by the reciprocal of the coefficient to both sides. **Remember that when you divide or multiply by a negative number that the inequality symbol changes. 5.)Solve for the variable.

Example 1 20 - 6c < 44

Example 1(Continued) 20 - 6c < 44 -20 -20 Add the opposite

Example 1 (continued) 20 - 6c < 44 -20 -20 Add the opposite

Example1 (Continued) 20 - 6c < 44 -20 -20 Add the opposite -6c < 24 Divide by the coefficient -6 -6

Example 1 (Continued 20 - 6c < 44 -20 -20 Add the opposite -6c < 24 Divide by the coefficient -6 -6 Switch symbol(divided by neg. #) c > -4 Solution graph

Example 2 5m – 4 < 2m + 11

Example 2 (Continued) 5m – 4 < 2m + 11 -2m -2m Add the opp.

Example 2 (Continued) 5m – 4 < 2m + 11 -2m -2m Add the opp

Example 2 (Continued) 5m – 4 < 2m + 11 -2m -2m Add the opp

Example 2 ( Continued) 5m – 4 < 2m + 11 -2m -2m Add the opp 3m < 15 Divide by 3 3 3

Example 2 ( continued) 5m – 4 < 2m + 11 -2m -2m Add the opp 3m < 15 Divide by 3 3 3 m < 5 Solution graph

Solving Compound Inequalities A compound inequality is two simple inequalities joined by “and” or “or”.

Example 3 Solving an “and” compound inequality Graph solution

Example 4 Solving an “or” compound inequality Graph solution

Example 5 Milk will keep until its expiration date and will not freeze when stored at a minimum temperature of and a maximum temperature of . The temperature C satisfies the inequality Write the inequality in Fahrenheit.

Example 6 The feeding instructions on your dog’s food recommend 2½ to 3¼ lb of food weekly. Write the conditions that represent underfeeding or overfeeding your dog as a compound inequality. Rewrite the conditions in ounces of dog food (1 lb = 16 oz).

Example 7 The percent of households h with cable television is modeled by h = 2.3y + 44, where y is the number of years since 1998. Describe the years when the percent in less than 53.2.