Question

find the real solutions of 9-l2xl=2

Answer 1

Answer

x = -7/2, 7/2

Step-by-step explanation

Given the equation:

$9-|2x|=2$

Subtracting 9 at both sides of the equation:

$\begin{gathered} 9-9-\lvert2x\rvert=2-9 \\ -\lvert2x\rvert=-7 \end{gathered}$

Dividing by -1 at both sides of the equation:

$\begin{gathered} \frac{-\lvert2x\rvert}{-1}=\frac{-7}{-1} \\ |2x|=7 \end{gathered}$

Now we have two options:

$\begin{gathered} 2x=7 \\ \text{ Or} \\ 2x=-7 \end{gathered}$

Solving the first option:

$\begin{gathered} 2x_1=7 \\ \frac{2x_1}{2}=\frac{7}{2} \\ x_1=\frac{7}{2} \end{gathered}$

Solving the second option:

$\begin{gathered} 2x_2=-7 \\ \frac{2x_2}{2}=\frac{-7}{2} \\ x_2=-\frac{7}{2} \end{gathered}$