Question

Find the solution of this inequality. Enter your answer on interval notation using grouping symbols.

Answer 1

$|4x-6|\leq14$

apply the absolute rule,

$\begin{gathered} -(4x-6)\leq14 \\ 4x-6\leq14 \end{gathered}$

solve each inequality independently,

$\begin{gathered} \text{ divide both sides by -1 and switch the sign, } \\ 4x-6\ge-14 \\ \text{ solve for x} \\ 4x\ge-8 \\ x\ge-\frac{8}{4} \\ x\ge-2 \end{gathered}$$\begin{gathered} 4x-6\leq14 \\ 4x\leq20 \\ x\leq\frac{20}{4} \\ x\leq5 \end{gathered}$

find the intersection of both solutions

$\begin{gathered} x\ge-2\rightarrow\lbrack-2,\infty) \\ x\leq5\rightarrow(-\infty,5\rbrack \\ \lbrack-2,\infty)\cap(-\infty,5\rbrack\rightarrow\lbrack-2,5\rbrack \end{gathered}$

Answer:

The solution to the inequality in interval notation is:

$\lbrack-2,5\rbrack$