Question

solve and graph the following
3 < x + 7 < 15

Explanation:

Step1: Isolate x in the left - hand side inequality

Subtract 7 from all parts of the compound inequality \(3

Step2: Isolate x in the right - hand side inequality

For the right - hand side, \(x+7 - 7<15 - 7\), which simplifies to \(x<8\).

Answer:

The solution is \(-4 < x<8\). To graph it on a number line, draw an open circle at \(-4\) (because \(x\) is greater than \(-4\) but not equal to it), draw an open circle at \(8\) (because \(x\) is less than \(8\) but not equal to it), and shade the region between \(-4\) and \(8\).