We have the inequality -23 < 4x-7. Our aim is to have X on its own on the left of the inequality sign:
It is important to remember that every operation performed, must be performed on each side of the inequality, in this first step we are adding 7 on the right side and subtracting 7 on the left side.
[tex]\begin{gathered} -23+7<4x-7+7 \\ -16<4x \end{gathered}[/tex]We are going to pass x from the right side to the left side, by doing this we must also change the direction of the inequality:
[tex]4x>-16[/tex]Then we divide by 4 on each side:
[tex]\begin{gathered} \frac{4x}{4}>\frac{-16}{4} \\ x>-4 \end{gathered}[/tex]