What is 1/11 |2x-4|+10<= 11 ?

The solution to 1/11 |2x-4|+10<= 11 is -7/2 <= x<= 15/2

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1/11 |2x-4|+10<= 11

\frac{1}{11} ∣ 2 x - 4 ∣ + 10 \leq 11

- \frac{7}{2} \leq x \leq \frac{15}{2}

Interval Notation

[- \frac{7}{2}, \frac{15}{2}]

Decimal Notation

- 3.5 \leq x \leq 7.5

Solution steps

\frac{1}{11} ∣ 2 x - 4 ∣ + 10 \leq 11

Move

10

to the right side

\frac{1}{11} ∣ 2 x - 4 ∣ \leq 1

Multiply both sides by

11

∣ 2 x - 4 ∣ \leq 11

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 11 \leq 2 x - 4 \leq 11

2 x - 4 \geq - 11 and 2 x - 4 \leq 11

x \geq - \frac{7}{2} and x \leq \frac{15}{2}

Merge Overlapping Intervals

- \frac{7}{2} \leq x \leq \frac{15}{2}

4 x^{2} - 25

∣ 7 + p ∣ = 7

\frac{1}{4} + \frac{1}{6}

4. 5^{2}

What is 1/11 |2x-4|+10<= 11 ?
The solution to 1/11 |2x-4|+10<= 11 is -7/2 <= x<= 15/2