What is -2|5x+2|+4<= 3 ?

The solution to -2|5x+2|+4 =-3/10

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

- 2 ∣ 5 x + 2 ∣ + 4 \leq 3

x \leq - \frac{1}{2} or x \geq - \frac{3}{10}

Interval Notation

(- \infty, - \frac{1}{2}] \cup [- \frac{3}{10}, \infty)

Decimal Notation

x \leq - 0.5 or x \geq - 0.3

Solution steps

- 2 ∣ 5 x + 2 ∣ + 4 \leq 3

Move

4

to the right side

- 2 ∣ 5 x + 2 ∣ \leq - 1

Multiply both sides by

- 1

2 ∣ 5 x + 2 ∣ \geq 1

Divide both sides by

2

∣ 5 x + 2 ∣ \geq \frac{1}{2}

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

5 x + 2 \leq - \frac{1}{2} or 5 x + 2 \geq \frac{1}{2}

5 x + 2 \leq - \frac{1}{2} or 5 x + 2 \geq \frac{1}{2}

x \leq - \frac{1}{2} or x \geq - \frac{3}{10}

n^{2} - 11 n + 30

- 3 (- 3 x - 1) + 2 x + 2 = 27

\frac{1 2 ^{3}}{1 2 ^{7}}

\frac{( m ^{5} n ^{5} ) ^{\frac{1}{6}}}{3 ( mn ) ^{- \frac{1}{6}}}

(24 c)^{\frac{2}{3}}

What is -2|5x+2|+4<= 3 ?
The solution to -2|5x+2|+4<= 3 is x<=-1/2 \lor x>=-3/10