Solving two step Inequalities

1. < > < < Solving two step Inequalities < < < >

2. Solving an Inequality • Follow the same rules and steps that we used to solve an equation. • Always undo addition or subtraction first, then multiplication or division. • Remember whatever is done to one side of the inequality must be done to the other side. The goal is to get the variable by itself.

3. -25 -20 -15 -10 -5 0 5 10 15 20 25 Examples 2h + 8 ≤ 24 -8 -8 2h ≤ 16 2 2 h ≤ 8 All numbers less than 8 (including 8)

4. Remember! There is one special case. • Sometimes you may have to reverse the direction of the inequality sign!! • That only happens when you multiply or divide both sides of the inequality by a negative number.

5. -6 0 Example: • Subtract 5 from each side. • Divide each side by negative 3. • Reverse the inequality sign. • Graph the solution. • Open circle, line to the left. Solve:-3y + 5 >23 -5-5 -3y > 18 -3 -3 y < -6

6. -25 -20 -15 -10 -5 0 5 10 15 20 25 Example: • Add 6 to each side. • Multiply each side by negative 2. • Reversethe inequality sign. Solve: < 3 +6+6 × -2 x > -18 < 9 • Graph the solution. • Open circle, line to the right.

7. -25 -20 -15 -10 -5 0 5 10 15 20 25 Example 2x + 3 ≥ 7 *Get the variable term alone* -3 -3 “undo” addition by subtraction 2 x ≥ 4 *Isolate the variable* 2 2 “undo” multiplication by division x ≥ 2 • Graph the solution. • Closed circle, line to the right.

8. -25 -20 -15 -10 -5 0 5 10 15 20 25 Example: • Subtract 6 from each side. • Multiply each side by . • Graph the solution. • Open circle, line to the left. Solve: < – 3 – 6– 6 < – 9 < – 9 x < – 15

9. Your Turn…. • x > –12 • x < 30 • c >– 3 • Solve the inequality and graph the answer. • x + 4 > – 4 • +8 < 14 • – 2c –4 ≤ 2

10. -25 -20 -15 -10 -5 0 5 10 15 20 25 Variable on the right… 14 > 3x – 4 +4 +4 18 > 3x 3 3 6> x = x<6 All numbers less than 6

11. Practice Solving two step equations