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Popular >

4|x-4|+6<= 30

Solution

4 ∣ x - 4 ∣ + 6 \leq 30

Solution

- 2 \leq x \leq 10

+1

Interval Notation

[- 2, 10]

Solution steps

4 ∣ x - 4 ∣ + 6 \leq 30

Move

6

to the right side

4 ∣ x - 4 ∣ \leq 24

Divide both sides by

4

∣ x - 4 ∣ \leq 6

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 6 \leq x - 4 \leq 6

x - 4 \geq - 6 and x - 4 \leq 6

x \geq - 2 and x \leq 10

Merge Overlapping Intervals

- 2 \leq x \leq 10

Popular Examples

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3 x^{2} + 2 x + 10 = 0

x^{2} + 2 x = 10 x + 140

Frequently Asked Questions (FAQ)

What is 4|x-4|+6<= 30 ?
The solution to 4|x-4|+6<= 30 is -2<= x<= 10