For this case we have the following equation:
[tex]\frac {5} {6} (2x + 12) -8 = 4- (x + 1)[/tex]
We apply distributive property on the left side of the equation:
[tex]\frac {5 * 2} {6} x + \frac {5 * 12} {6} -8 = 4- (x + 1)\\\frac {10} {6} x + \frac {60} {6} -8 = 4- (x + 1)[/tex]
We simplify the left side of the equation:
[tex]\frac {5} {3} x + 10-8 = 4- (x + 1)[/tex]
Different signs are subtracted and the major sign is placed.
[tex]\frac {5} {3} x + 2 = 4- (x + 1)[/tex]
On the right side we must take into account that:
[tex]- * + = -[/tex]
So:
[tex]\frac {5} {3} x + 2 = 4-x-1\\\frac {5} {3} x + 2 = 3-x[/tex]
We add x to both sides of the equation:
[tex]\frac {5} {3} x + x + 2 = 3\\\frac {5 * 1 + 3 * 1} {3} x + 2 = 3\\\frac {5 + 3} {3} x + 2 = 3\\\frac {8} {3} x + 2 = 3[/tex]
We subtract 2 from both sides of the equation:
[tex]\frac {8} {3} x = 3-2\\\frac {8} {3} x = 1[/tex]
We multiply by 3 on both sides of the equation:
[tex]8x = 3[/tex]
We divide by 8 on both sides of the equation:
[tex]x = \frac {3} {8}[/tex]
Thus, the solution of the equation is:
[tex]x = \frac {3} {8}[/tex]
Answer:
[tex]x = \frac {3} {8}[/tex]
