Question

1° Resolva em R as equações modulares:
A) |2x - 3| = 1

B) |4x - 1| - |2x + 3| = 0

Answer 1

A) $|2x-3|=1$

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

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B) $|4x-1|-|2x+3|=0$

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