Question

5/6(2x+12)-8=4-(x+1)

Answer 1

For this case we have the following equation:

$\frac {5} {6} (2x + 12) -8 = 4- (x + 1)$

We apply distributive property on the left side of the equation:

$\frac {5 * 2} {6} x + \frac {5 * 12} {6} -8 = 4- (x + 1)\\\frac {10} {6} x + \frac {60} {6} -8 = 4- (x + 1)$

We simplify the left side of the equation:

$\frac {5} {3} x + 10-8 = 4- (x + 1)$

Different signs are subtracted and the major sign is placed.

$\frac {5} {3} x + 2 = 4- (x + 1)$

On the right side we must take into account that:

$- * + = -$

So:

$\frac {5} {3} x + 2 = 4-x-1\\\frac {5} {3} x + 2 = 3-x$

We add x to both sides of the equation:

$\frac {5} {3} x + x + 2 = 3\\\frac {5 * 1 + 3 * 1} {3} x + 2 = 3\\\frac {5 + 3} {3} x + 2 = 3\\\frac {8} {3} x + 2 = 3$

We subtract 2 from both sides of the equation:

$\frac {8} {3} x = 3-2\\\frac {8} {3} x = 1$

We multiply by 3 on both sides of the equation:

$8x = 3$

We divide by 8 on both sides of the equation:

$x = \frac {3} {8}$

Thus, the solution of the equation is:

$x = \frac {3} {8}$

Answer:

$x = \frac {3} {8}$