Solve 2x+5x/8-x-5/6=x-4/2-4x+7/12

$$\frac{ 2x+5x }{ 8 } - \frac{ x-5 }{ 6 } = \frac{ x-4 }{ 2 } - \frac{ 4x+7 }{ 12 }$$

Solve for x

$$x = -\frac{82}{13} = -6\frac{4}{13} \approx -6.307692308$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 8,6,2,12.

$$3\left(2x+5x\right)-4\left(x-5\right)=12\left(x-4\right)-2\left(4x+7\right)$$

Combine 2x and 5x to get 7x.

$$3\times 7x-4\left(x-5\right)=12\left(x-4\right)-2\left(4x+7\right)$$

Multiply 3 and 7 to get 21.

$$21x-4\left(x-5\right)=12\left(x-4\right)-2\left(4x+7\right)$$

Use the distributive property to multiply -4 by x-5.

$$21x-4x+20=12\left(x-4\right)-2\left(4x+7\right)$$

Combine 21x and -4x to get 17x.

$$17x+20=12\left(x-4\right)-2\left(4x+7\right)$$

Use the distributive property to multiply 12 by x-4.

$$17x+20=12x-48-2\left(4x+7\right)$$

Use the distributive property to multiply -2 by 4x+7.

$$17x+20=12x-48-8x-14$$

Combine 12x and -8x to get 4x.

$$17x+20=4x-48-14$$

Subtract 14 from -48 to get -62.

$$17x+20=4x-62$$

Subtract 4x from both sides.

$$17x+20-4x=-62$$

Combine 17x and -4x to get 13x.

$$13x+20=-62$$

Subtract 20 from both sides.

$$13x=-62-20$$

Subtract 20 from -62 to get -82.

$$13x=-82$$

Divide both sides by 13.

$$x=\frac{-82}{13}$$

Fraction \frac{-82}{13} can be rewritten as -\frac{82}{13} by extracting the negative sign.

$$x=-\frac{82}{13}$$