What is -5|-x+7|+4>-45 ?

The solution to -5|-x+7|+4>-45 is -14/5 <x< 84/5

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-5|-x+7|+4>-45

- 5 ∣ - x + 7 ∣ + 4 > - 45

- \frac{14}{5} < x < \frac{84}{5}

Interval Notation

(- \frac{14}{5}, \frac{84}{5})

Decimal Notation

- 2.8 < x < 16.8

Solution steps

- 5 ∣ - x + 7 ∣ + 4 > - 45

Move

4

to the right side

- 5 ∣ - x + 7 ∣ > - 49

Multiply both sides by

- 1

5 ∣ - x + 7 ∣ < 49

Divide both sides by

5

∣ - x + 7 ∣ < \frac{49}{5}

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- \frac{49}{5} < - x + 7 < \frac{49}{5}

- x + 7 > - \frac{49}{5} and - x + 7 < \frac{49}{5}

x < \frac{84}{5} and x > - \frac{14}{5}

Merge Overlapping Intervals

- \frac{14}{5} < x < \frac{84}{5}

1^{0}

(x - 1)^{2} = 2

x - 5 x - 11 = 11 - 12 x - 9

(4 + 8 i)^{2}

\frac{( 4 - 2 x )}{3 x + 2} \leq 0