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Popular >

4|x-5|+1<= 3

Solution

4 ∣ x - 5 ∣ + 1 \leq 3

Solution

\frac{9}{2} \leq x \leq \frac{11}{2}

+2

Interval Notation

[\frac{9}{2}, \frac{11}{2}]

Decimal Notation

4.5 \leq x \leq 5.5

Solution steps

4 ∣ x - 5 ∣ + 1 \leq 3

Move

1

to the right side

4 ∣ x - 5 ∣ \leq 2

Divide both sides by

4

∣ x - 5 ∣ \leq \frac{1}{2}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{2} \leq x - 5 \leq \frac{1}{2}

x - 5 \geq - \frac{1}{2} and x - 5 \leq \frac{1}{2}

x \geq \frac{9}{2} and x \leq \frac{11}{2}

Merge Overlapping Intervals

\frac{9}{2} \leq x \leq \frac{11}{2}

Popular Examples

6 \geq 6

∣ x + 3 ∣ = x + 5

- u^{2} + 32 = 0

simplify-14/4 simplify

- \frac{14}{4}

x^{2} - x - 100 = - x

Frequently Asked Questions (FAQ)

What is 4|x-5|+1<= 3 ?
The solution to 4|x-5|+1<= 3 is 9/2 <= x<= 11/2