Problem:
What is the solution of l2x+9l=7
The solution are {-1, -8}
Explanation:
[tex]\textsf{The absolute value of a number is \text{de}fined by:}[/tex]
[tex]|x| = \begin{cases} \ \: \:x \quad \text{if }x \geq 0 \\ -x \quad \text{if }x < 0 \end{cases}[/tex]
[tex]\textsf{Thus,}[/tex]
[tex]2x+9 = \begin{cases} \ \: \:7 \quad \text{if }x \geq 0 \\ -7 \quad \text{if }x < 0 \end{cases}[/tex]
[tex]\textsf{Consider the cases below.}[/tex]
[tex]\begin{array}{l | l} \bold{Case \: 1 }\text{:} \ x \geq 0 & \bold{Case \: 2 }\text{:} \ x < 0\\\textsf{The equation becomes} & \textsf{The equation becomes}\\2x + 9 = 7 & 2x + 9 = -7\\2x = -2 & 2x = -16\\x = -1 & x = -8\end{array}[/tex]
[tex]\therefore x = \{-1,-8\}[/tex]
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