These twenty problems practice Common Core 7.EE.B.4b: solving two-step inequalities of the form \(px+q>r\) and \(px+q< r\), graphing each solution set, and reading the answer in context. The first problems keep the coefficients positive. Later problems introduce negative coefficients and finish with word problems about money, weight, temperature and height.
Problem 1: Solve and graph
Solve \(2x+3>11\). Graph the solution on the number line.
Problem 2: Greater than
Solve \(3x+2>17\). Graph the solution on the number line.
Problem 3: Subtract, then divide
Solve \(3x-5< 10\). Graph the solution on the number line.
Problem 4: Less than
Solve \(4x-6< 10\). Graph the solution on the number line.
Problem 5: Include the endpoint
Solve \(4x+7\ge 23\). Then test one value from your solution set to check it.
Problem 6: Include the endpoint, again
Solve \(2x+9\ge 3\). Graph the solution on the number line.
Problem 7: At most
Solve \(5x-2\le 18\). Graph the solution on the number line.
Problem 8: Test the values
Solve \(3x-4\le 11\). Then tell which of the values \(x=3\), \(x=5\) and \(x=6\) are solutions.
Problem 9: A fraction coefficient
Solve \(\frac{x}{2}+3>7\).
Problem 10: Divide by five
Solve \(\frac{x}{5}-1\le 2\).
Problem 11: Dividing by a negative
Solve \(-2x+1< 9\). Graph the solution on the number line.
Problem 12: Flip the sign
Solve \(-4x+3>19\). Graph the solution on the number line.
Problem 13: Negative coefficient, closed circle
Solve \(-3x-4\ge 5\). Describe the graph of the solution set.
Problem 14: Negative fraction
Solve \(-\frac{1}{2}x-3\le 2\).
Problem 15: School store budget
Jamal has \(\$50\) to spend at the school store. He buys a cap for \(\$12\) and then some T-shirts at \(\$9\) each. Write and solve an inequality for the number of shirts \(s\). What is the greatest number of shirts he can buy?
Problem 16: Dog walking goal
Priya earns $12 for each hour she walks dogs and has already received $35 in tips. She wants to have at least $200. Write and solve an inequality for the number of hours \(h\). What is the least whole number of hours she must walk dogs?
Problem 17: Delivery van
A delivery van can carry at most \(1,000\) pounds. The driver and the equipment weigh \(220\) pounds, and each box weighs \(40\) pounds. Write and solve an inequality for the number of boxes \(b\). What is the greatest number of boxes the van can carry?
Problem 18: Freezer temperature
A freezer is at \(10^{\circ}\text{F}\) and cools by \(3^{\circ}\text{F}\) every hour. Write and solve an inequality to find when the temperature is below \(-8^{\circ}\text{F}\). Let \(h\) be the number of hours.
Problem 19: Drone descent
A drone flies at \(120\text{ ft}\) and descends \(15\text{ ft}\) every second. It must stay at least \(30\text{ ft}\) above the ground. Write and solve an inequality for the number of seconds \(s\) it can descend.
Problem 20: Bake sale profit
Priya sells boxes of cookies for \(\$2.50\) each at a bake sale. She spent \(\$20\) on ingredients and wants a profit of at least \(\$85\). Write and solve an inequality for the number of boxes \(b\). What is the least number of boxes she must sell?
See every chapter on the Grade 7 math page.