What is | x/4-1|-1<= 1/4 ?

The solution to | x/4-1|-1<= 1/4 is -1<= x<= 9

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| x/4-1|-1<= 1/4

\frac{x}{4} - 1 - 1 \leq \frac{1}{4}

- 1 \leq x \leq 9

Interval Notation

[- 1, 9]

Solution steps

\frac{x}{4} - 1 - 1 \leq \frac{1}{4}

Move

1

to the right side

\frac{x}{4} - 1 \leq \frac{5}{4}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{5}{4} \leq \frac{x}{4} - 1 \leq \frac{5}{4}

\frac{x}{4} - 1 \geq - \frac{5}{4} and \frac{x}{4} - 1 \leq \frac{5}{4}

x \geq - 1 and x \leq 9

Merge Overlapping Intervals

- 1 \leq x \leq 9

\frac{5}{2 3}

3 a + 8 = 14

z \leq 0 and z \geq 2

20 < 6 x - 1

m^{2} - 6 m + 8 = 0