Given:
[tex]8-2(2x+9)<42[/tex]
Step 1:
Collect like terms
Thus, we have
[tex]\begin{gathered} -2(2x+9)<42-8 \\ -2(2x+9)<34 \end{gathered}[/tex]
Step 2:
Open the brackets in the Left Hand Side of the inequality.
[tex]\begin{gathered} -2(2x+9)<34 \\ -2(2x)+(-2(9))<34 \\ \Rightarrow-4x-18<34 \end{gathered}[/tex]
Step 3:
Collect like terms
[tex]\begin{gathered} -4x-18<34 \\ -4x<34+18 \\ -4x<52 \end{gathered}[/tex]
Step 4:
Divide both sides of the inequality by the coefficient of x.
The coefficient of x is -4.
Thus,
[tex]\begin{gathered} \frac{-4x}{-4}<\frac{52}{-4} \\ \Rightarrow x>-13 \end{gathered}[/tex]
When the coefficient of an unknown is a negative number, and is to be used to divide both sides of the inequality, the signs are changed.
Thus, the solution to the inequality is
[tex]x>-13[/tex]
