These 22 problems practice Common Core standards A-REI.B.3, A-CED.A.1 and A-CED.A.3. Solve multi-step inequalities, remember to reverse the sign when dividing by a negative, graph solutions and write interval notation, and work with compound inequalities joined by and or or. The last six are word problems that ask for an inequality first.
Problem 1: One-step graph
Solve \(3x+4>19\) and graph the solution.
Problem 2: Closed circle
Solve \(5x-7\le28\) and graph the solution.
Problem 3: Divide by a negative
Solve \(-2x+9< 15\).
Problem 4: Distribute and solve
Solve \(4(x-3)\ge2x+6\).
Problem 5: Variables on both sides
Solve \(7-3x>2x-8\).
Problem 6: Fraction coefficient
Solve \(\frac{x}{3}-2\le4\).
Problem 7: Negative fraction
Solve \(-\frac{2}{3}x\ge8\).
Problem 8: Negative outside parentheses
Solve \(-2(x+4)< 6\).
Problem 9: Fractions on both sides
Solve \(\frac{x+1}{2}\ge\frac{2x-1}{3}\).
Problem 10: Decimal inequality
Solve \(0.6x-1.5< 0.2x+2.5\).
Problem 11: All or none
Solve each inequality.
- \(3(x+2)>3x+1\)
- \(2x+5< 2x-1\)
Problem 12: Read the graph
Write an inequality and interval notation for each graph.
Problem 13: Compound with and
Solve \(-3< 2x+1\le9\) and graph the solution.
Problem 14: Compound with or
Solve \(2x-1<-5\text{ or }3x+2\ge11\) and graph the solution.
Problem 15: Three-part inequality
Solve \(4\le3x-2< 13\).
Problem 16: Overlap of two conditions
Solve \(x+3>1\text{ and }2x\le10\).
Problem 17: School store budget
Diego has \(\$50\). A backpack costs \(\$18.50\) and each T-shirt costs \(\$6.25\). Write and solve an inequality for the number of T-shirts \(t\) he can add. What is the greatest whole number?
Problem 18: Weekend job
Aisha earns \(\$12\) per hour and pays \(\$15\) for bus fare. She wants to take home at least \(\$150\). How many hours must she work?
Problem 19: Elevator limit
An elevator holds at most 1,200 pounds. Liam loads a cart that weighs 180 pounds and boxes that weigh 35 pounds each. How many boxes can he load?
Problem 20: Car rental
Rental company A charges \(\$30\) per day plus \(\$0.20\) per mile. Company B charges \(\$45\) per day with unlimited miles. For how many miles in one day is A cheaper?
Problem 21: Test average
Mei scored 88, 92 and 85 on three tests. She wants an average of at least 90 after the fourth test, and the highest possible score is 100. Write a compound inequality for her fourth score \(s\).
Problem 22: Saving up
Sofia has \(\$35\) and saves \(\$5\) each week. After how many weeks will she have between \(\$100\) and \(\$150\), inclusive?
See every chapter on the Algebra 1 math page.