Solve |3x - 2| ≥ 4: Absolute Value Inequality Challenge

Because absolute value measures distance! When $|3x - 2| \geq 4$, it means the expression 3x - 2 is either 4 or more units to the right of zero, or 4 or more units to the left of zero.

For $|A| \geq B$, always use 'or' because solutions are on opposite sides of the number line. For $|A| \leq B$, use 'and' because solutions are between two values.

If B is negative in $|A| \geq B$, then all real numbers are solutions! Absolute values are never negative, so they're always ≥ any negative number.

Yes! Graph $y = |3x - 2|$ and $y = 4$. The solution includes all x-values where the absolute value graph is on or above the horizontal line y = 4.

This is a ≥ inequality, not ≤! The solution includes values outside the boundary points $x = -\frac{2}{3}$ and $x = 2$, not between them.