Solve and Graph With Negative Coefficients

Teach the sign flip with One-Step Inequalities With Negative Coefficients after the addition and multiplication sheets. The maze and Match Solutions to Graphs work well as an exit check because a wrong answer leads nowhere.

Solve and graph eight inequalities with negative coefficients, such as −12x > 54 and −0.4x ≤ 2.8. The directions on the page read: Solve each inequality and graph the solution. When you multiply or divide both sides by a negative number, flip the inequality sign. Read each number line's labels to see what one tick is worth. 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.

Undo the operation on x by doing the inverse on both sides, just as with an equation. For x + 21 < 8, subtract 21 from each side to get x < −13. Write the answer with x first.

Multiplying or dividing by a negative number reverses the order of numbers on the number line. So −4x > 26 becomes x < −6.5 after dividing by −4. The sign must flip to keep the statement true.

Solve first, then graph the answer. In the example on the graphing sheet, x/3 < 2.5 gives x < 7.5, shown with an open circle at 7.5 and a ray to the left.