Solving and Graphing Inequalities

Algebra 1 · Axiom Academy

LESSON Solving & Graphing Inequalities The rules for manipulating an inequality are the rules for an equation — with one twist that flips everything. Just like an equation, you can add or subtract the same number on both sides of an inequality and the statement stays true. The symbol does not change. Watch the entire solution slide along the number line as we add 4 to both sides of x - 4 < 3 . 2. Multiplying or Dividing by a Positive You can also multiply or divide both sides by the same positive number. Scaling by a positive keeps every point on the same side of zero, so the order is unchanged and the symbol stays the same. Watch the solution set for shrink toward zero as we divide by 3. 3. The One Rule to Remember: Negative Means Flip This is the special rule. When you multiply or divide both sides by a negative number, you must flip the inequality symbol . Multiplying by a negative reflects every point across zero — which reverses their order on the line. Watch 4 < 6 become -4 > -6 when both sides are multiplied by -1 . 4. Graphing the Solution: Open vs. Closed Once solved, we draw the solution on a number line. The endpoint tells the whole story. A strict inequality ( < or > ) uses an open circle — the boundary is a limit but is not itself a solution. An inequality with "or equal to" ( or ) uses a closed circle — the boundary is included. Watch both endpoints draw at the boundary value 3 .

This is the written version of the interactive lesson above. See the full Algebra 1 course.