Answer:
[tex](-\infty,-2)[/tex]
Step-by-step Explanation:
Given the below;
[tex]2(3x+2)<-2x-12[/tex]
We'll follow the below steps to solve for x;
Step 1: Clear the parentheses on the left-hand side by expansion;
[tex]6x+4<-2x-12[/tex]
Step 2: Subtract 4 from both sides;
[tex]\begin{gathered} 6x<-2x-12-4 \\ 6x<-2x-16 \end{gathered}[/tex]
Step 3: Add 2x to both sides;
[tex]\begin{gathered} 6x+2x<-16 \\ 8x<-16 \end{gathered}[/tex]
Step 4: Divide both sides by 8;
[tex]\begin{gathered} \frac{8x}{8}<\frac{-16}{8} \\ x<-2 \end{gathered}[/tex]
We can see from the above that the solution to the inequality are all values of x that are less than -2, so we can go ahead and write the solution using interval notation as seen below;
[tex](-\infty,-2)[/tex]
