Question

Solve the inequality. Then graph its solution. $$3 x-2>4 \text { or } 3 x-2<-5$$

Short answer

The solution to the inequality is \(x < -1\) or \(x > 2\). These are all numbers that are less than -1 or greater than 2.

Step-by-step solution

Solve the first inequality

The first inequality is \(3x - 2 > 4\). By adding 2 to both sides gives \(3x > 6\). Dividing both sides by 3 results in \(x > 2\).

Solve the second inequality

The second inequality is \(3x - 2 < -5\). Adding 2 to both sides gives \(3x < -3\). Dividing both sides by 3 results in \(x < -1\).

Combine and interpret solutions

The 'or' connector allows to group all values that satisfy either inequality. Hence, the solution to the inequality is \(x < -1\) or \(x > 2\). The solution includes all values that are less than -1 or greater than 2.

Graph Solutions

In a number line, mark the points -1 and 2 and color the regions to the left of -1 and to the right of 2. This coloring represents all numbers less than -1 and greater than 2.