Variables on Both Sides Riddle

Start with Inequalities With Variables on Both Sides, then add negatives and parentheses. Use Always, Never or Sometimes True for discussion, and the riddle or maze for practice that checks itself.

Solve nine inequalities with x on both sides and decode a riddle about what the triangle said to the circle. The directions on the page read: Solve each inequality in its box. Find the solution in the bank and write its letter in the box with the same number below. The page opens with a worked example, and an answer key is included.

Yes, both. We made it for 8th grade algebra, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

Subtract one x term from both sides so x is on only one side, then solve the two-step inequality left. For 6x − 1 > 2x + 31, subtract 2x to get 4x − 1 > 31, so 4x > 32 and x > 8.

Yes. If the x terms cancel and a true statement is left, every value works. For 3(x + 1) > 3x + 2, the sides simplify to 3 > 2, which is always true. If a false statement is left, no value works.

Collect the decimal x terms the same way as whole numbers. For 0.3x ≤ 1.3x + 11, subtracting 1.3x gives −x ≤ 11, and dividing by −1 flips the sign to x ≥ −11.