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|x − 4| + 3x = x - 2

User Pawan Rao
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1 Answer

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The absolute value of a number is the number or the negative of the number

Example will be shown in the equation below


\lvert{x}\rvert=\begin{cases}={x} \\ ={-x}\end{cases}

the value of x will be two ......i will show the first solution now


\begin{gathered} \lvert{x-4}\rvert+3x=x-2 \\ \lvert{x-4}\rvert=x-2-3x \\ \lvert x-4\rvert=-2-2x \\ x-4=-2-2x \\ x+2x=-2+4 \\ 3x=2 \\ x=(2)/(3) \end{gathered}

the first solution was interpreted using absolute value of a number to be the number

the next solution i will show you now will be interpreted using absolute value of a number to be the negative of the number


\begin{gathered} \lvert{x-4}\rvert=x-2-3x \\ \lvert{x-4}\rvert=-2x-2 \\ -(x-4)=-2x-2 \\ -x+4=-2x-2 \\ -x+2x=-2-4 \\ x=-6 \end{gathered}

The final answers are x=-6 , and x=2/3

User Akzy
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