Solving -2x + 3 > 7

Pre-Algebra · Axiom Academy

EXAMPLE Solving a Multi-Step Inequality Solve step by step, and master the one rule that trips everyone up: flipping the sign when you divide by a negative. Solve the inequality for x . Isolate the variable with inverse operations, then state the full solution set. Here is what looks like on a number line. The open circle at −2 shows that −2 is not included in the solution. Every value to the left (less than −2) is a solution. Nice work. You solved a multi-step inequality the same way you would an equation — with one extra rule to watch for. Work step by step: use inverse operations to isolate the variable, just as you would with an equation. The flip rule is critical: multiplying or dividing both sides by a negative number flips the inequality symbol ( becomes , becomes ). Why it flips: , but dividing both by -2 gives — the relationship reverses. Open vs. closed circle: use an open circle for or , a closed circle for or .

This is the written version of the interactive lesson above. See the full Pre-Algebra course.