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Popular >

|2x+1|+1<= 8

Solution

∣ 2 x + 1 ∣ + 1 \leq 8

Solution

- 4 \leq x \leq 3

+1

Interval Notation

[- 4, 3]

Solution steps

∣ 2 x + 1 ∣ + 1 \leq 8

Move

1

to the right side

∣ 2 x + 1 ∣ \leq 7

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 7 \leq 2 x + 1 \leq 7

2 x + 1 \geq - 7 and 2 x + 1 \leq 7

x \geq - 4 and x \leq 3

Merge Overlapping Intervals

- 4 \leq x \leq 3

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4(x-3)+8=4(2x-6)

4 (x - 3) + 8 = 4 (2 x - 6)

Frequently Asked Questions (FAQ)

What is |2x+1|+1<= 8 ?
The solution to |2x+1|+1<= 8 is -4<= x<= 3