Writing Inequalities from Word Problems

Master writing inequalities from word problems! Practice budgets, costs, and more.

1-4) Match the phrase to the correct inequality symbol. "at most" or = (greater than or equal to) "larger than" > "below" < 5) ATT has a family plan of four lines for $125 and additional lines are $15 each per month. If Jason wants to spend at most $200 per month on cell phone expenses, how many additional lines can he afford? 125 + 15𝒙 ≥ 200 125 + 15𝒙 ≤ 200 125 − 15𝒙 ≥ 200 125 − 15 ≤ 200 6) Jannie has a budget of $200 to spend on jeans and shirts. She spends $75 on jeans. If the cost of each shirtis $19.50, how many can she buy without going over the budget? 19.50𝒙 + 75 ≤ $200 75𝒙 + 19.50 ≤ $200 19.50𝒙 - 75 ≥ $200 75𝒙 -19.50 ≥ $200 7) Ten more than three times a number is no more than -95. What could be the value of the number? 10 + 3𝒙 ≤ −95 10 + 3𝒙 ≥ −95 3𝒙 - 10 ≤ −95 3𝒙 - 10 ≥ −95 8-10) Matching Inequalities Match the example with the correct inequality. Joseph has 20 gallons of gas in his tank. His tank uses 6 gallons an hour. Choose the inequality that represents the length of time Joseph can drive before running out of gas. 6x ≥ 20 Joseph must sell more than 20 ice cream cones in order to make a profit. He has already sold 6 cones. Choose the inequality that represents the number of cones Joseph still needs to sell. x + 6 ﹥20 Joseph withdraws $25 each week for 10 weeks for entertainment. He wants to have more than $200 remaining by the end of the summer. Choose the inequality that represents the amount of money Joseph started the summer with. x - 250 ﹥200 11) An AC technician charges an inspection fee of $150 plus $45 for every labor hour. If Julie has a budget of$425, what is the maximum number of hours can she hire the AC technician? 150𝒙 + 45 ≥ 425 150𝒙 − 45 ≥ 425 150 −45𝒙 ≤ 425 150+45𝒙 ≤ 425 12) A certain cell phone company has a monthly base charge of $17.99 plus seven cents per minute used. Dwaine’s monthly budget for cell phone expenses is $74.75. How many minutes can he use without exceeding his budget? 17.99x - 0.7 ≥ 74.75 17.99 - 0.7𝒙 ≤ 74.75 17.99+ 0.7x ≤ 74.75 17.99 - 0.7𝒙 ≥ 74.75 13) The distance between Jaime' house and his destination is at most 933 miles. If he is driving at a speed of 65 mph and has traveled 120 miles, in how many hours can he expected to be at his destination, assuming that his speed will remain constant? 933 ≤ 120 + 65𝒙 933 ≥ 120𝒙 + 65 933 ≤ 120𝒙 + 65 933 ≥120 + 65𝒙 14) Your brother has $2,000 saved for a vacation. His airplane ticket is $637. Write an inequality to find out how much he can spend for everything else. 2000 ≤ x + 637 2000 ≥ x + 637 2000 + 637 ≤ x 2000 + 637 ≥ x 15) Which statement can be modeled by x + 3 ≤ 12? Sam has 3 bottles of water. Together, Sam and Dave have at most 12 bottles of water. Jennie sold 3 cookbooks. To earn a prize, Jennie must sell at least 12 cookbooks. Peter has 2 baseball hats. Peter and his brothers have fewer than 12 baseball hats. Kathy swam 3 laps in the pool this week. She must swim more than 12 laps. 16) Addie works in New York City and makes $42 per hour. She works in an office and must get her suit dry cleaned everyday for $75. If she wants to make more than $260 a day, write an inequality to represent the situation. 42x + 75 ≥ 260 42x - 75 ≤ 260 42x - 75 ≥ 260 42x + 75 ≤ 260 17) For a field trip 18 students rode in cars and the rest filled five buses. If no more than 250 students went on the field trip, write an inequality to represent the situation. 18 + 5x ≤ 250 18x + 5 ≤ 250 18 + 5x ≥ 250 18x + 5 ≥ 250 18) Charles is saving $5 each week. He earns an extra $15 by mowing his neighbor's lawn. How many weeks will he need to save in order to have at least $75? Write an inequality for the situation. 5 + 15x ≥ 75 5 + 15x ≤ 75 5x + 15 ≤ 75 5x + 15 ≥ 75 19) Mark's Canoes rents canoes for $20 plus $35 per hour. You do not want to spend more than $150. Write an inequality to represent the situation. 20x + 35 ≥ 150 20 + 35x ≥ 150 20 + 35x ≤ 150 20x + 35 ≤ 150 20) Bill spent less than $26 on a magazine and five composition books. The magazine cost $4. Write an inequality to represent the situation. 4 + 5x < 26 4x + 5 < 26 4 + 5x > 26 4x + 5 > 26