4.2

Solving Inequalities using ADD or SUB

4.2 – Solving Inequalities

Goals / “I can…”Use addition to solve inequalitiesUse subtraction to solve inequalities

1) Which inequality would have a closed dot on the number line?

1. >

2. <

3. ≥

4. ≠

Answer NowAnswer Now

2) Which inequality does NOT use an open dot on the number line?

1. ≤

2. <

3. >

4. ≠

Answer NowAnswer Now

4.2 – Solving Inequalities

Solving an inequality (<, >, ≤, ≥) is just like solving an equality (=). The concept of balancing a scale is the same.

4.2 – Solving Inequalities

Example:Solve x + 3 = -6

4.2 – Solving Inequalities

solve x + 3 < -6

6) Solve x + (-14) < 16

x - 14 < 16

+ 14 + 14

x < 30

30 + (-14) = 16

16 = 16

Solve this problem like an equation

1. Draw “the river”2. Eliminate double

signs3. Add 14 to both sides4. Simplify5. Check your answer6. Graph the solution

o30 3129

7) Solve y + 21 ≥ 7

- 21 -21

y ≥ -14

(-14) + 21 = 7

7 = 7

1. Draw the “river”2. Subtract 21 from

both sides3. Simplify4. Check your answer5. Graph the solution

-14 -13-15●

8) Solve 8y + 3 > 9y - 14

o17 1816

- 8y - 8y

3 > y - 14

+ 14 + 14

17 > y

y < 178(17) + 3 = 9(17) - 14

1. Draw “the river”

2. Subtract 8y from both sides

3. Simplify

4. Add 14 to both sides

5. Simplify

6. Rewrite inequality with the variable first

7. Check your answer

8. Graph the solution

4.2 – Solving Inequalities

Solve x – 4 = 12

4.2 – Solving Inequalities

solve x – 4 > 12