What is |((2x-4))/(-6)|+2<= 10 ?

The solution to |((2x-4))/(-6)|+2<= 10 is -22<= x<= 26

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|((2x-4))/(-6)|+2<= 10

\frac{( 2 x - 4 )}{- 6} + 2 \leq 10

- 22 \leq x \leq 26

Interval Notation

[- 22, 26]

Solution steps

\frac{2 x - 4}{- 6} + 2 \leq 10

Move

2

to the right side

\frac{2 x - 4}{- 6} \leq 8

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 8 \leq \frac{2 x - 4}{- 6} \leq 8

\frac{2 x - 4}{- 6} \geq - 8 and \frac{2 x - 4}{- 6} \leq 8

x \leq 26 and x \geq - 22

Merge Overlapping Intervals

- 22 \leq x \leq 26

∣ z - 1 ∣ + ∣ z + 1 ∣ \leq 3

∣ 2 x + 3 ∣ > \frac{1}{2}

\frac{2 x - 3}{x - 1} > 3

\frac{( x + 1 )}{( x - 1 )} < 1

∣ x - 2 ∣ \leq ∣ x - 4 ∣

What is |((2x-4))/(-6)|+2<= 10 ?
The solution to |((2x-4))/(-6)|+2<= 10 is -22<= x<= 26