Question

Se o número ½ é solução da equação

3.(x-1) - ⅖ . (x+4) = m . (x - 2) + ½ . (x + 3)

na variável x, então o valor de m é

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Answer 1

$3(x-1)-\frac{2}{5} .(x+4)= m . (x-2) + \frac{1}{2}.(x+3) \\\\ 3(\frac{1}{2} -1)-\frac{2}{5} .(\frac{1}{2} +4)= m . (\frac{1}{2} -2) + \frac{1}{2}.(\frac{1}{2} +3) \\\\\frac{3}{2} -3-\frac{2}{10} -\frac{8}{5}= \frac{m}{2} -2m+\frac{1}{4} +\frac{3}{2} \\\\\frac{30-60-4-32=10m-40m+5+30}{20} \\\\\\30-60-4-32=10m-40m+5+30\\\\-10m+40m = 5+30+32+4+60-30\\\\30m = 101\\\\m = \frac{101}{30}$