Multi-step Inequalities Worksheet with Answer Key

What's on the worksheet

1. Solve each inequality and write the answer with the variable first.
   5x + 3 < 2x - 124 - 3n \ge n + 208p - 9 > 11p + 6-2y + 7 \le -6y - 171.5w + 4 \ge 0.5w + 1
2. Clear parentheses, fractions or decimals first, then solve each inequality.
   3(x - 4) \le 5x + 22(3a + 1) - a > 4(a - 2)7 - 2(m + 5) \ge 3(m - 6)\dfrac{x - 6}{4} < \dfrac{x}{6} + 2\dfrac{2}{5}(t + 10) \ge t - 2
3. Solve each inequality and say if every real number or no number is a solution when the variable vanishes.
   5(x + 1) - 2x < 3(x + 2)4(2 - x) \ge 2(3 - 2x) + 32(x - 3) \le 3x - 2(x + 1)6x - 2(x + 3) \ge 4(x - 1) - 2
4. Check Kevin's steps in solving an inequality and fix his sign handling.
5. Compare the perimeter of a square and an equilateral triangle to find the values of x.
6. Hannah and Carlos each save weekly: find when Hannah has less than Carlos.
7. Solve an inequality with a letter coefficient, first for a given value, then find the value that fits a condition.