Solve 2(x+1)/2+3(x-1)/3+8(x+2)/4=5x

$$\frac { 2 ( x + 1 ) } { 2 } + \frac { 3 ( x - 1 ) } { 3 } + \frac { 8 ( x + 2 ) } { 4 } = 5 x$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4.

$$6\times 2\left(x+1\right)+4\times 3\left(x-1\right)+3\times 8\left(x+2\right)=60x$$

Multiply 6 and 2 to get 12.

$$12\left(x+1\right)+4\times 3\left(x-1\right)+3\times 8\left(x+2\right)=60x$$

Use the distributive property to multiply 12 by x+1.

$$12x+12+4\times 3\left(x-1\right)+3\times 8\left(x+2\right)=60x$$

Multiply 4 and 3 to get 12.

$$12x+12+12\left(x-1\right)+3\times 8\left(x+2\right)=60x$$

Use the distributive property to multiply 12 by x-1.

$$12x+12+12x-12+3\times 8\left(x+2\right)=60x$$

Combine 12x and 12x to get 24x.

$$24x+12-12+3\times 8\left(x+2\right)=60x$$

Subtract 12 from 12 to get 0.

$$24x+3\times 8\left(x+2\right)=60x$$

Multiply 3 and 8 to get 24.

$$24x+24\left(x+2\right)=60x$$

Use the distributive property to multiply 24 by x+2.

$$24x+24x+48=60x$$

Combine 24x and 24x to get 48x.

$$48x+48=60x$$

Subtract 60x from both sides.

$$48x+48-60x=0$$

Combine 48x and -60x to get -12x.

$$-12x+48=0$$

Subtract 48 from both sides. Anything subtracted from zero gives its negation.

$$-12x=-48$$

Divide both sides by -12.

$$x=\frac{-48}{-12}$$

Divide -48 by -12 to get 4.

$$x=4$$