Section 2.11 : Linear Inequalities
3. Solve the following inequality and give the solution in both inequality and interval notation.
\[ - 1 < 4x + 2 < 10\]Show All Steps Hide All Steps
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, let’s start by subtracting 2 from all the parts. This gives,
\[ - 3 < 4x < 8\] Show Step 2Finally, all we need to do is divide all three parts by 4 to get,
\[ - \frac{3}{4} < x < 2\]So, the inequality form of the solution is \(\require{bbox} \bbox[2pt,border:1px solid black]{{ - \frac{3}{4} < x < 2}}\) and the interval notation form of the solution is \(\require{bbox} \bbox[2pt,border:1px solid black]{{\left( { - \frac{3}{4},2} \right)}}\) .