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

The solution to 2<= |4-5x|<= 4 is 0<= x<= 2/5 \lor 6/5 <= x<= 8/5

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

2 \leq ∣ 4 - 5 x ∣ \leq 4

0 \leq x \leq \frac{2}{5} or \frac{6}{5} \leq x \leq \frac{8}{5}

Interval Notation

[0, \frac{2}{5}] \cup [\frac{6}{5}, \frac{8}{5}]

Decimal Notation

0 \leq x \leq 0.4 or 1.2 \leq x \leq 1.6

Solution steps

2 \leq ∣ 4 - 5 x ∣ \leq 4

a \leq u \leq b

then

a \leq u and u \leq b

2 \leq ∣ 4 - 5 x ∣ and ∣ 4 - 5 x ∣ \leq 4

2 \leq ∣ 4 - 5 x ∣ : x \leq \frac{2}{5} or x \geq \frac{6}{5}

∣ 4 - 5 x ∣ \leq 4 : 0 \leq x \leq \frac{8}{5}

Combine the intervals

(x \leq \frac{2}{5} or x \geq \frac{6}{5}) and 0 \leq x \leq \frac{8}{5}

Merge Overlapping Intervals

0 \leq x \leq \frac{2}{5} or \frac{6}{5} \leq x \leq \frac{8}{5}

\frac{5}{2} \cdot \frac{1}{2}

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

x^{2} \geq 121

81 x^{2} - 36 x + 4

8 y - 36

What is 2<= |4-5x|<= 4 ?
The solution to 2<= |4-5x|<= 4 is 0<= x<= 2/5 \lor 6/5 <= x<= 8/5