Question

Solve, graph and write the solution in interval notation: |6x−5|<7

Answer 1

The given inequality is,

$|6x-5|<7$

According to absolute rule,

$|y|0 then y>-a and y}Applying absolute rule to the given inequality, [tex]6x-5>-7\text{ and }6x-5<7$

Solving 6x-5>-7,

$\begin{gathered} 6x-5>-7 \\ 6x>-7+5 \\ 6x>-2 \\ x>\frac{-2}{6} \\ x>\frac{-1}{3} \end{gathered}$

Solving 6x-5<7,

$\begin{gathered} 6x-5<7 \\ 6x<7+5 \\ 6x<12 \\ x<\frac{12}{6} \\ x<2 \end{gathered}$

So, the solution is x>-1/3 and x<2.

The solution in interval notation is (-1/3, 2).

Now, the graph of the inequality is,

(Hollow dot in the graph indicates open interval).