What is |x+3|>|x-6| ?

The solution to |x+3|>|x-6| is x> 3/2

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|x+3|>|x-6|

∣ x + 3 ∣ > ∣ x - 6 ∣

x > \frac{3}{2}

Interval Notation

(\frac{3}{2}, \infty)

Decimal Notation

x > 1.5

Solution steps

∣ x + 3 ∣ > ∣ x - 6 ∣

Find positive and negative intervals

x < - 3, - 3 \leq x < 6, x \geq 6

Solve the inequality for each interval

No Solution or \frac{3}{2} < x < 6 or x \geq 6

Merge Overlapping Intervals

x > \frac{3}{2}

- x^{2} + 8 x - 19 = 0

u^{2} + u - 20 = 0

x^{2} + 14 + 24

C - 12 = - 24

4 + \frac{x + 5}{8} = 20