Answer: [tex]\x = \frac{3}{4} = 0.75[/tex]
1. We need to find common denominator. In this case it is 6:
[tex]
\frac{2x + 7}{6} + \frac{x - 5 * 2}{3 * 2} = 0
\\ \\ \\
\frac{2x + 7}{6} + \frac{2x - 10}{6} = 0
[/tex]
2. Now we multiply by 6, so denominator disappears:
[tex]
\frac{2x + 7}{6} * 6 + \frac{2x - 10}{6} * 6 = 0
\\ \\ \\
2x + 7 + 2x - 10 = 0
\\ \\ \\
4x - 3 = 0
\\ \\ \\
4x = 3 |:4
\\ \\ \\
X = \frac{3}{4}[/tex] = 0.75
So answer is [tex]\frac{3}{4}[/tex]. Proof:
[tex]
\frac{2 * 0.75 + 7}{6} + \frac{0.75 - 5}{3} =
\\ \\ \\
\frac{1.5 + 7}{6} + \frac{-4.25 * 2}{3 * 2} =
\\ \\ \\
\frac{8.5}{6} + \frac{-8.5}{6} =
\\ \\ \\
\frac{8.5}{6} - \frac{8.5}{6} = 0[/tex]
So this answer is right, if both sides are same.
