147 views
13 votes
13 votes
Solve the absolute value equation l2x+3l+4=1

User Surckarter
by
2.9k points

1 Answer

29 votes
29 votes

The given equation is


|2x+3|+4=1

First, we need to isolate the absolute value, we'll subtract 4 one each side


\begin{gathered} |2x+3|+4-4=1-4 \\ |2x+3|=-3 \end{gathered}

Now, we rewrite the equation in two equations


\begin{gathered} 2x+3=-3 \\ 2x+3=-(-3)\rightarrow2x+3=3 \end{gathered}

Let's solve each equation


\begin{gathered} 2x+3=-3 \\ 2x=-3-3 \\ 2x=-6 \\ x=-(6)/(2)=-3 \end{gathered}

So, the first solution is -3.


\begin{gathered} 2x+3=3 \\ 2x=3-3=0 \\ x=(0)/(2)=0 \end{gathered}

The second solution is zero.

Therefore, the solutions are -3, and 0.

User Joery
by
3.2k points