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Popular >

5|-4x+2|-3<= 27

Solution

5 ∣ - 4 x + 2 ∣ - 3 \leq 27

Solution

- 1 \leq x \leq 2

+1

Interval Notation

[- 1, 2]

Solution steps

5 ∣ - 4 x + 2 ∣ - 3 \leq 27

Move

3

to the right side

5 ∣ - 4 x + 2 ∣ \leq 30

Divide both sides by

5

∣ - 4 x + 2 ∣ \leq 6

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 6 \leq - 4 x + 2 \leq 6

- 4 x + 2 \geq - 6 and - 4 x + 2 \leq 6

x \leq 2 and x \geq - 1

Merge Overlapping Intervals

- 1 \leq x \leq 2

Popular Examples

h + 15 = 25

x+(x+2)=28+(x+4)

x + (x + 2) = 28 + (x + 4)

- \frac{x}{2} \geq - \frac{x}{4} + 1

2+2/5 (x+1)=x-(2x+3)/5

2 + \frac{2}{5} (x + 1) = x - \frac{2 x + 3}{5}

x^{2} \leq 4 x

Frequently Asked Questions (FAQ)

What is 5|-4x+2|-3<= 27 ?
The solution to 5|-4x+2|-3<= 27 is -1<= x<= 2