Question

Sketch the graph of the inequality. $$x+3>-2$$

Short answer

The solution to the inequality \(x+3>-2\) is \(x>-5\), indicating all values greater than -5. On the graph, an open dot at -5 followed by shading to the right represents the solution.

Step-by-step solution

Identify the Inequality

Observe the inequality \(x+3>-2\). This is a single-variable inequality and our goal is to find all possible values of \(x\) that make this inequality true.

Solve the Inequality for Variable \(x\)

To solve the inequality for \(x\), subtract 3 from both sides. This gives us \(x>-2-3\), simplifying to \(x>-5\). So all values of \(x\) greater than -5 will satisfy the inequality.

Graphing the Inequality

Draw a number line and mark the point -5 on it. Since the inequality is \(x>-5\), we want all values of \(x\) greater than -5, not including -5. So we use an open dot at -5. And then shade all the points to the right of -5, indicating these are the \(x\) values satisfying the inequality.