1. Section 4 Solving Inequalities
Chapter 1
Section 4
Solving Inequalities

2. Inequalities The solutions include more than one number
Ex: 2 < x ;values that x could be include 3, 7, 45…
All of the rules for solving equations apply to inequalities, with one added:
If you multiply or divide by a NEGATIVE you must FLIP the sign. (< becomes > and > becomes <)
When graphing on a number line:
Open dot for < or >
Closed (solid) dot for ≤ or ≥
The shading should be easy to see (a slightly elevated line is ok) --- see examples

3. Solving Inequalities –2x < 3(x – 5)
ALGEBRA 2 LESSON 1-4
Solve –2x < 3(x – 5). Graph the solution.
–2x < 3(x – 5)
–2x < 3x – 15 Distributive Property
–5x < –15 Subtract 3x from both sides.
x > 3 Divide each side by –5 and reverse the inequality.

4. Inequalities – Special Solution Cases
If the variables cancel, and you’re left with a true statement (ex. 0<10) then all numbers are solutions for the inequality.
If the variables cancel, and you’re left with a false statement (ex. 0>10) then no numbers are solutions for the inequality.

5. Solve 7x ≥ 7(2 + x). Graph the solution.
7x ≥ x Distributive Property
0 ≥ 14 Subtract 7x from both sides.
The last inequality is always false, so 7x ≥ 7(2 + x) is always false. It has no solution.

6. Compound Inequalities - Disjuctions
Compound Inequality – a pair of inequalities joined by or
For or statements the value must satisfy one of the inequalities
Example: x < -1 or x ≥ 3

7. Or Inequalities
ALGEBRA 2 LESSON 1-4
Graph the solution of 3x + 9 < –3 or –2x + 1 < 5.
3x + 9 < –3 or –2x + 1 < 5
3x < – or x < 4
x < –4 or x > –2

8. Try This Problem Graph the solution of x – 1 < 3 or x - 3 > 8

9. Compound Inequalities - Conjuctions
A pair of inequalities joined by an and statement
The value must satisfy both inequalities.
In other words, the solution is where the inequalities overlap.
Can be written in two forms:
Example: -1 < x and x ≤ 3 is the same as -1 < x ≤ 3

10. And Inequalities
Graph the solution of 3x – 1 > -28 and 2x + 7 < 19.
3x > -27 and 2x < 12
x > -9 and x < 6
Graph the solution of -8 < 3x + 1 <19
-9 < 3x < 18
-3 < x < 6

11. Check for Understanding
Graph the solution of 2x > x + 6 and x – 7 < 2
x > 6 and x < 9