What is ((|x|+4))/((|x|+3))>= 0 ?

The solution to ((|x|+4))/((|x|+3))>= 0 is True for all x

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((|x|+4))/((|x|+3))>= 0

\frac{( ∣ x ∣ + 4 )}{( ∣ x ∣ + 3 )} \geq 0

True for all x

Solution steps

\frac{∣ x ∣ + 4}{∣ x ∣ + 3} \geq 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x < 0 or x \geq 0

Merge Overlapping Intervals

True for all x

∣ x - 1 ∣ < ∣ x ∣

x^{2} + x + ∣ x ∣ + 1 < 0

∣ x + 1 ∣ + ∣ x ∣ > 3

x^{2} + x + ∣ x ∣ + 1 \leq 0

x^{2} - 1 < ∣ 2 x - 1 ∣

What is ((|x|+4))/((|x|+3))>= 0 ?
The solution to ((|x|+4))/((|x|+3))>= 0 is True for all x