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Popular >

5|x+3|+1<= 41

Solution

5 ∣ x + 3 ∣ + 1 \leq 41

Solution

- 11 \leq x \leq 5

+1

Interval Notation

[- 11, 5]

Solution steps

5 ∣ x + 3 ∣ + 1 \leq 41

Move

1

to the right side

5 ∣ x + 3 ∣ \leq 40

Divide both sides by

5

∣ x + 3 ∣ \leq 8

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 8 \leq x + 3 \leq 8

x + 3 \geq - 8 and x + 3 \leq 8

x \geq - 11 and x \leq 5

Merge Overlapping Intervals

- 11 \leq x \leq 5

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Frequently Asked Questions (FAQ)

What is 5|x+3|+1<= 41 ?
The solution to 5|x+3|+1<= 41 is -11<= x<= 5