What is |1-x|-|4+x|<0 ?

The solution to |1-x|-|4+x| -3/2

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|1-x|-|4+x|<0

∣ 1 - x ∣ - ∣ 4 + x ∣ < 0

x > - \frac{3}{2}

Interval Notation

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

Decimal Notation

x > - 1.5

Solution steps

∣ 1 - x ∣ - ∣ 4 + x ∣ < 0

Find positive and negative intervals

x < - 4, - 4 \leq x \leq 1, x > 1

Solve the inequality for each interval

No Solution or - \frac{3}{2} < x \leq 1 or x > 1

Merge Overlapping Intervals

x > - \frac{3}{2}

∣ x + 1 ∣ > 1

∣ x - 13 ∣ \leq - 2

\frac{25 ( ∣ x + 3 ∣ + x )}{( x + 2 )} > 1

x + 2 - x^{2} \leq x^{2} - 3 x + 4

(\frac{( ∣ x + 1 ∣ + 5 )}{∣ 2 - x ∣}) > 5