Solve 12-x+2/4=5-10x/8+9x+1/3

$$12 - \frac { x + 2 } { 4 } = \frac { 5 - 10 x } { 8 } + \frac { 9 x + 1 } { 3 }$$

Solve for x

$$x = \frac{253}{48} = 5\frac{13}{48} \approx 5.270833333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 4,8,3.

$$288-6\left(x+2\right)=3\left(5-10x\right)+8\left(9x+1\right)$$

Use the distributive property to multiply -6 by x+2.

$$288-6x-12=3\left(5-10x\right)+8\left(9x+1\right)$$

Subtract 12 from 288 to get 276.

$$276-6x=3\left(5-10x\right)+8\left(9x+1\right)$$

Use the distributive property to multiply 3 by 5-10x.

$$276-6x=15-30x+8\left(9x+1\right)$$

Use the distributive property to multiply 8 by 9x+1.

$$276-6x=15-30x+72x+8$$

Combine -30x and 72x to get 42x.

$$276-6x=15+42x+8$$

Add 15 and 8 to get 23.

$$276-6x=23+42x$$

Subtract 42x from both sides.

$$276-6x-42x=23$$

Combine -6x and -42x to get -48x.

$$276-48x=23$$

Subtract 276 from both sides.

$$-48x=23-276$$

Subtract 276 from 23 to get -253.

$$-48x=-253$$

Divide both sides by -48.

$$x=\frac{-253}{-48}$$

Fraction \frac{-253}{-48} can be simplified to \frac{253}{48} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{253}{48}$$