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Popular >

4|x-3|-6<10

Solution

4 ∣ x - 3 ∣ - 6 < 10

Solution

- 1 < x < 7

+1

Interval Notation

(- 1, 7)

Solution steps

4 ∣ x - 3 ∣ - 6 < 10

Move

6

to the right side

4 ∣ x - 3 ∣ < 16

Divide both sides by

4

∣ x - 3 ∣ < 4

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 4 < x - 3 < 4

x - 3 > - 4 and x - 3 < 4

x > - 1 and x < 7

Merge Overlapping Intervals

- 1 < x < 7

Popular Examples

|2x-5|-3|x-5|+|4-x|>= 3x+5

∣ 2 x - 5 ∣ - 3 ∣ x - 5 ∣ + ∣ 4 - x ∣ \geq 3 x + 5

|(2x-1)/(x-1)|>2

\frac{2 x - 1}{x - 1} > 2

x^{2} - ∣ 5 x - 3 ∣ - x > 2

9 - 2 ∣ 4 x + 1 ∣ > 3

x+|3-2x|>|x+1|-1

x + ∣ 3 - 2 x ∣ > ∣ x + 1 ∣ - 1

Frequently Asked Questions (FAQ)

What is 4|x-3|-6<10 ?
The solution to 4|x-3|-6<10 is -1<x<7