Question

4|2x + 5|-7≤9

How would you solve this?

Answer 1

-
`(9)/(2)` ≤ x ≤ -
`(1)/(2)`

Explanation:

inequalities of the type | x | ≤ a , have solutions of the form

- a ≤ x ≤ a , then

4 | 2x + 5 | - 7 ≤ 9 ( add 7 to both sides )

4 | 2x + 5 | ≤ 16 ( divide both sides by 4 )

| 2x + 5 | ≤ 4 , so

- 4 ≤ 2x + 5 ≤ 4 ( subtract 5 from each interval )

- 9 ≤ 2x ≤ - 1 ( divide each interval by 2 )

-
`(9)/(2)` ≤ x ≤ -
`(1)/(2)`

Answer 2

solate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
−
9
2
≤
x
≤
−
1
2
-
9
2
≤
x
≤
-
1
2
Interval Notation:
[
−
9
2
,
−
1
2
]