What is -2|x-5|+7>= 4 ?

The solution to -2|x-5|+7>= 4 is 7/2 <= x<= 13/2

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-2|x-5|+7>= 4

- 2 ∣ x - 5 ∣ + 7 \geq 4

\frac{7}{2} \leq x \leq \frac{13}{2}

Interval Notation

[\frac{7}{2}, \frac{13}{2}]

Decimal Notation

3.5 \leq x \leq 6.5

Solution steps

- 2 ∣ x - 5 ∣ + 7 \geq 4

Move

7

to the right side

- 2 ∣ x - 5 ∣ \geq - 3

Multiply both sides by

- 1

2 ∣ x - 5 ∣ \leq 3

Divide both sides by

2

∣ x - 5 ∣ \leq \frac{3}{2}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{3}{2} \leq x - 5 \leq \frac{3}{2}

x - 5 \geq - \frac{3}{2} and x - 5 \leq \frac{3}{2}

x \geq \frac{7}{2} and x \leq \frac{13}{2}

Merge Overlapping Intervals

\frac{7}{2} \leq x \leq \frac{13}{2}

8 x - 4 > 4 x + 16

n^{2} = - 14 n - 37

8 a^{2} - 120 a + 576 = 0

2 x^{2} + 3 x + 6 = 0

3 x^{2} + x + 7 = 0