Question

Solve the inequality. Then graph the solution. $$|2 x+3|>4$$

Short answer

The solution is \(x > 0.5\) and \(x < -3.5\). The graph is a number line with shaded regions to the right of 0.5 and to the left of -3.5.

Step-by-step solution

Consider the Case Where \(2x+3 > 4\)

Subtract 3 from both sides of the inequality: \(2x > 4 - 3\), then divide both sides by 2: \(x > (4-3)/2\). Solve to get \(x > 0.5\).

Consider the Case Where \(2x+3 < -4\)

Again, subtract 3 from both sides of the inequality: \(2x < -4 - 3\), then divide both sides by 2: \(x < (-4-3)/2\). Solve to get \(x < -3.5\).

Graph the Solution

The graph will consist of two halves of the number line. To graph \(x > 0.5\), make a dotted line at \(x = 0.5\) and shade the region to the right of it. For \(x < -3.5\), make a dotted line at \(x = -3.5\) and shade the region to the left of it.