Multi-Step Inequalities With Negative Coefficients

Use Solve Multi-Step Inequalities and Multi-Step Inequalities With Like Terms first, then the graphing sheets. The word problem sheets fit after students are steady with the algebra, and the maze and matching sheet work as a check.

Distribute negative factors to solve 12 inequalities like −3(x + 2) > 9, flipping the sign where needed. The directions on the page read: Show your work and write the solution on the line. Watch for steps that flip the sign. 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.

Distribute to clear parentheses, combine like terms, then undo addition or subtraction and finally multiplication or division. For 4(x + 2) − 5 ≥ 35, simplify to 4x + 3 ≥ 35, so 4x ≥ 32 and x ≥ 8.

Multiply both sides by a common denominator. In the example, multiplying 1/3(x + 4) ≥ 5 by 3 gives x + 4 ≥ 15, so x ≥ 11. Multiplying by a positive number keeps the sign the same.

Look at what the question asks. A decimal answer of x ≥ 8.6 weeks means at least 9 weeks, while x ≤ 14.4 boxes means at most 14 boxes. Write, Solve and Interpret practices this choice.

Every term inside the parentheses changes sign, and later dividing by a negative coefficient flips the sign. So −2(x + 3) > 16 becomes −2x − 6 > 16, then x < −11.