Solve for x: x2 – 2x ³ 8 I will expand upon Method 1 like example 7 on page 137.
Solve
Step
x2 – x ³ 8
x2 – x – 8 ³ 0
(x – 4)(x+ 2) ³ 0
Check 
(-2 – 4)(-2+ 2) ³ 0
-6(0) = 0 ³
0
Check
(4 – 4)(4+ 2) ³ 0
0(6) = 0 ³ 0
Use -3, 0, and 5
|
Solve for x: x2 – 2x ³ 8 I will expand upon Method 1 like example 7 on page 137. |
|
|
Solve |
Step |
|
x2 – x ³ 8 |
First, get zero on one side. Both methods will fail if you forget this step. |
|
x2 – x – 8 ³ 0 |
Factor. Click here for help factoring. |
|
(x – 4)(x+ 2) ³ 0 |
Clearly, 4 and -2 are solutions. Because of ³ symbol. |
|
Check (-2 – 4)(-2+ 2) ³ 0 -6(0) = 0 ³
0 |
Check (4 – 4)(4+ 2) ³ 0 0(6) = 0 ³ 0 |
| Since this an inequality, we expect more solutions. | |
|
|
The solutions are broken up into these intervals |
|
Use -3, 0, and 5 |
Pick points in these intervals to see if they work. |
|
Test Points |
||
| if x = -3, then | ||
| (-3)2 – (-3) – 8 = 9 + 3 – 8 = 4 ³ 0 TRUE So (–¥, –2] works.** | ||
| if x = 0, then | ||
| (0)2 – (0) – 8 = 0 + 0 – 8 = –8 ³ 0 FALSE So [–2, 4] fails.** | ||
| if x = 5, then | ||
| (5)2 – (5) – 8 = 25 – 5 – 8 = 12 ³ 0 TRUE So [4, ¥) works.** | ||
|
Graph |
||
|
The solutions is
(–¥,
–2] È
[4, ¥) |
||
|
**Important: How do you know if the
Test Point works? Check the inequality symbol. x2 – x – 8 ³ 0 If the statement is true, it works. |
||
