Question

1. what is the solution to the inequality $2(3x + 9) < \frac{1}{3}(9x - 63)$?\

\bigcirc $x < -13$\
\bigcirc $x < -3$\
\bigcirc $x > -13$\
\bigcirc $x > -3$

Explanation:

Step1: Expand both sides

Left side: \(2(3x + 9)=6x + 18\)
Right side: \(\frac{1}{3}(9x - 63)=3x - 21\)
So the inequality becomes \(6x + 18<3x - 21\)

Step2: Subtract \(3x\) from both sides

\(6x - 3x+ 18<3x - 3x - 21\)
\(3x + 18<-21\)

Step3: Subtract 18 from both sides

\(3x + 18 - 18<-21 - 18\)
\(3x<-39\)

Step4: Divide both sides by 3

\(\frac{3x}{3}<\frac{-39}{3}\)
\(x<-13\)

Answer:

\(x < -13\) (corresponding to the option with text \(x < -13\))