Warm Up Solve each inequality. Graph and check the solution.
Find 3 possible solutions to the given inequalities.
Solving two-step inequalities is similar to solving two step equations. You must isolate the variable by performing the same operation on both sides of the inequality. The direction of the inequality symbol changes when both sides of the inequality are multiplied or divided by a negative number. It is important to distinguish between the phrases “greater than” and “greater than or equal to” and the phrases “less than” and “less than or equal to.”
During the year Ms. Torres paid $1,200 for car repairs and bought 4 new tires. The total amount she spent on her car for repairs and tires was less than $1,820. How much did each new tire cost? Justify your answer.
Ed wants to bicycle at least 75 miles this week. The inequality 11 + 4b ≥ 75 can be used to find b, the average number of miles he should bike on his remaining 4 bike rides this week. Solve the inequality, and graph the solution set on a number line.
Dianna is buying lunch for herself and two friends. She has a coupon for $15 off the total bill and wants to spend less than $49 after using the coupon. The equation 3m - 15 < 49 can be used to find m, the average price of each friend’s lunch. Determine which, if any, of the following values make the equation true: m = 21; m = 22; m = 23.