Question

2(3x + 2) < – 2x – 12write the solution using interval notation

Answer 1

Answer:

$(-\infty,-2)$

Step-by-step Explanation:

Given the below;

$2(3x+2)<-2x-12$

We'll follow the below steps to solve for x;

Step 1: Clear the parentheses on the left-hand side by expansion;

$6x+4<-2x-12$

Step 2: Subtract 4 from both sides;

$\begin{gathered} 6x<-2x-12-4 \\ 6x<-2x-16 \end{gathered}$

Step 3: Add 2x to both sides;

$\begin{gathered} 6x+2x<-16 \\ 8x<-16 \end{gathered}$

Step 4: Divide both sides by 8;

$\begin{gathered} \frac{8x}{8}<\frac{-16}{8} \\ x<-2 \end{gathered}$

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;

$(-\infty,-2)$