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

The solution to 4-1/2 |2x+1| = 5/2

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

4 - \frac{1}{2} ∣ 2 x + 1 ∣ \leq 1

x \leq - \frac{7}{2} or x \geq \frac{5}{2}

Interval Notation

(- \infty, - \frac{7}{2}] \cup [\frac{5}{2}, \infty)

Decimal Notation

x \leq - 3.5 or x \geq 2.5

Solution steps

4 - \frac{1}{2} ∣ 2 x + 1 ∣ \leq 1

Move

4

to the right side

- \frac{1}{2} ∣ 2 x + 1 ∣ \leq - 3

Multiply both sides by

- 1

\frac{1}{2} ∣ 2 x + 1 ∣ \geq 3

Multiply both sides by

2

∣ 2 x + 1 ∣ \geq 6

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

2 x + 1 \leq - 6 or 2 x + 1 \geq 6

2 x + 1 \leq - 6 or 2 x + 1 \geq 6

x \leq - \frac{7}{2} or x \geq \frac{5}{2}

2 x^{2} + 2 x - 40 = 0

6 + 2 i

- 5 x^{4} - 55 x^{3} + 60 x^{2}

2 x + 18 - 1 = 33

x^{2} - 14 x + 45

What is 4-1/2 |2x+1|<= 1 ?
The solution to 4-1/2 |2x+1|<= 1 is x<=-7/2 \lor x>= 5/2