Question

Find the real solutions of 9-l2xl=2

Answer 1

x = -7/2, 7/2

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} (-\lvert2x\rvert)/(-1)=(-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 \\ (2x_1)/(2)=(7)/(2) \\ x_1=(7)/(2) \end{gathered}`

Solving the second option:

`\begin{gathered} 2x_2=-7 \\ (2x_2)/(2)=(-7)/(2) \\ x_2=-(7)/(2) \end{gathered}`