Question

resolva as seguintes equações modulares

a) |x-3|=5
b) |2x-1|=7

Answer 1

a) $|x-3|=5$

$x-3=\pm 5\\\\ x=\pm 5+3\\\\ \begin{array}{rcl} x=-5+3&~\text{ ou }~&x=5+3 \end{array}\\\\ ~~~~~\boxed{\begin{array}{rcl} x=-2&~\text{ ou }~&x=8 \end{array}}$

Conjunto solução: $S=\{-2,\,8\}.$
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b) $|2x-1|=7$

$2x-1=\pm 7\\\\ 2x=\pm 7+1\\\\ x=\dfrac{\pm 7+1}{2}\\\\\\ \begin{array}{rcl} x=\dfrac{-7+1}{2}&~\text{ ou }~&x=\dfrac{7+1}{2}\\\\ x=\dfrac{-6}{2}&~\text{ ou }~&x=\dfrac{8}{2} \end{array}\\\\\\ ~~~~~~\boxed{\begin{array}{rcl} x=-3&~\text{ ou }~&x=4 \end{array}}$

Conjunto solução: $S=\{-3,\,4\}.$