Question

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Solve the equation. Check for extraneous solutions.
9|9 – 8x| = 2x + 3

Answer 1

`9-8x\geq0\ \ \ |subtract\ 9\ from\ both\ sides\\\\-8x\geq-9\ \ \ \ |change\ signs\\\\8x\leq9\ \ \ \ |divide\ both\ sides\ by\ 8\\\\x\leq9\\\\ |9-8x|=\left\{\begin{array}{ccc}9-8x&for\ x\leq9\\8x-9&for\ x \ \textgreater \ 9\end{array}\right`


`1^o\ x\in(-\infty;\ 9]\to|9-8x|=9-8x\\\\9(9-8x)=2x+3\\81-72x=2x+3\ \ \ \ |subtract\ 81\ from\ both\ sides\\-72x=2x-78\ \ \ \ |subtract\ 2x\ from\ both\ sides\\-74x=-78\ \ \ \ |divide\ both\ sides\ by\ (-74)\\\\x=(-78:2)/(-74:2)\\\\\boxed{x=(39)/(37)}\in(-\infty;\ 9]`


`2^o\ x\in(9;\ \infty)\to|9-8x|=8x-9\\\\9(8x-9)=2x+3\\72x-81=2x+3\ \ \ \ |add\ 81\ to\ both\ sides\\72x=2x+84\ \ \ \ |subtract\ 2x\ from\ both\ sides\\70x=84\ \ \ \ \ \ |divide\ both\ sides\ by\ 70\\\\x=(84:14)/(70:14)\\\\x=(6)/(5)\\otin(9;\ \infty)\\\\\\Answer:\boxed{x=(39)/(37)}`