Solve the Absolute Value Inequality: |5x - 2| < 3x + 8

The absolute value $|5x - 2|$ represents distance from zero. This distance can come from positive or negative values, so we need both cases: when 5x - 2 is positive and when it's negative.

When you have $5x - 2 > -(3x + 8)$, distribute the negative first: $5x - 2 > -3x - 8$. Then solve normally by collecting like terms.

You need both conditions to be true simultaneously. From $x < 5$ AND $x > -\frac{3}{4}$, the overlap gives us $-\frac{3}{4} < x < 5$.

Yes! If the right side becomes negative or zero, like $|x| < -2$, there's no solution because absolute values are always non-negative.

Pick a test value from your solution interval, like $x = 0$. Substitute: $|5(0) - 2| = 2$ and $3(0) + 8 = 8$. Since 2 < 8, our solution works!