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### Section 2.11 : Linear Inequalities

5. Solve the following inequality and give the solution in both inequality and interval notation.

$0 \le 10w - 15 \le 23$

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Hint : Solving double inequalities uses the same basic process as solving single inequalities. Just remember that what you do to one part you have to do to all parts of the inequality.
Start Solution

Just like with single inequalities solving these follow pretty much the same process as solving a linear equation. The only difference between this and a single inequality is that we now have three parts of the inequality and so we just need to remember that what we do to one part we need to do to all parts.

Also, recall that the main goal is to get the variable all by itself in the middle and all the numbers on the two outer parts of the inequality.

So, letâ€™s start by add 15 to all the parts. This gives,

$15 \le 10w \le 38$ Show Step 2

Finally, all we need to do is divide all three parts by 10 to get,

$\frac{3}{2} \le w \le \frac{{19}}{5}$

So, the inequality form of the solution is $$\require{bbox} \bbox[2pt,border:1px solid black]{{\frac{3}{2} \le w \le \frac{{19}}{5}}}$$ and the interval notation form of the solution is $$\require{bbox} \bbox[2pt,border:1px solid black]{{\left[ {\frac{3}{2},\frac{{19}}{5}} \right]}}$$ .