What is |x+2|+|3x+5|>= 2 ?

The solution to |x+2|+|3x+5|>= 2 is x =-5/4

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|x+2|+|3x+5|>= 2

∣ x + 2 ∣ + ∣ 3 x + 5 ∣ \geq 2

x \leq - \frac{9}{4} or x \geq - \frac{5}{4}

Solution steps

∣ x + 2 ∣ + ∣ 3 x + 5 ∣ \geq 2

Find positive and negative intervals

x < - 2, - 2 \leq x < - \frac{5}{3}, x \geq - \frac{5}{3}

Solve the inequality for each interval

x \leq - \frac{9}{4} or No Solution or x \geq - \frac{5}{4}

Merge Overlapping Intervals

x \leq - \frac{9}{4} or x \geq - \frac{5}{4}

∣ 3 x + 2 ∣ > ∣ 2 x - 1 ∣

x + (\frac{2}{x}) < 3

x^{2} - 3 x + x - 2 > 0

\frac{( x ^{2} - ∣ x ∣ - 2 )}{( 2 ∣ x ∣ - x ^{2} - 2 )} > 2

∣ 3 d - 3 ∣ > 12

What is |x+2|+|3x+5|>= 2 ?
The solution to |x+2|+|3x+5|>= 2 is x<=-9/4 \lor x>=-5/4