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}`