Solving -2x + 5 > 11

Algebra 1 · Axiom Academy

EXAMPLE Solving a Two-Step Inequality Solve the inequality -2x + 5 > 11 and uncover the most important rule for inequalities. Solve the inequality -2x + 5 > 11 for x . Work it one step at a time, watching carefully for the moment the inequality sign must flip. x < -3 is every number to the left of -3 . The open circle shows -3 itself is not included. Nice work — you solved the inequality and handled the rule that trips most people up. Isolate the variable term first: undo the +5 with subtraction to get -2x alone. The flip rule: dividing (or multiplying) both sides by a negative number reverses the inequality sign — here > became < . Result: -2x + 5 > 11 gives x < -3 , the whole set of numbers to the left of -3 on the number line. Forgetting to flip the sign when dividing by a negative is the single most common inequality mistake — catch it and the rest is just algebra.

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