Solve x+4/5-(x/6+3)=4x-40x-7/10

$$\frac { x + 4 } { 5 } - ( \frac { x } { 6 } + 3 ) = 4 x - \frac { 40 x - 7 } { 10 }$$

Solve for x

$$x=87$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,6,10.

$$6\left(x+4\right)-30\left(\frac{x}{6}+3\right)=120x-3\left(40x-7\right)$$

Use the distributive property to multiply 6 by x+4.

$$6x+24-30\left(\frac{x}{6}+3\right)=120x-3\left(40x-7\right)$$

Use the distributive property to multiply -3 by 40x-7.

$$6x+24-30\left(\frac{x}{6}+3\right)=120x-120x+21$$

Combine 120x and -120x to get 0.

$$6x+24-30\left(\frac{x}{6}+3\right)=21$$

Multiply both sides of the equation by 6.

$$6\left(6x+24\right)-180\left(\frac{x}{6}+3\right)=126$$

Multiply both sides of the equation by 6.

$$36\left(6x+24\right)-6\times 180\left(\frac{x}{6}+3\right)=756$$

Use the distributive property to multiply 36 by 6x+24.

$$216x+864-6\times 180\left(\frac{x}{6}+3\right)=756$$

Multiply -6 and 180 to get -1080.

$$216x+864-1080\left(\frac{x}{6}+3\right)=756$$

Use the distributive property to multiply -1080 by \frac{x}{6}+3.

$$216x+864-1080\times \frac{x}{6}-3240=756$$

Cancel out 6, the greatest common factor in 1080 and 6.

$$216x+864-180x-3240=756$$

Combine 216x and -180x to get 36x.

$$36x+864-3240=756$$

Subtract 3240 from 864 to get -2376.

$$36x-2376=756$$

Add 2376 to both sides.

$$36x=756+2376$$

Add 756 and 2376 to get 3132.

$$36x=3132$$

Divide both sides by 36.

$$x=\frac{3132}{36}$$

Divide 3132 by 36 to get 87.

$$x=87$$