Solve 10x/10+11+5-3x/3-13/6=6x+25/2+frac{3x}{5}frac{38}{4}

$$\frac { 10 x } { 10 } + 11 + \frac { 5 - 3 x } { 3 } - \frac { 13 } { 6 } = \frac { 6 x + 25 } { 2 } + \frac { 3 x } { 5 } \frac { 38 } { 4 }$$

Solve for x

$$x=-\frac{20}{87}\approx -0.229885057$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 10,3,6,2,5,4.

$$6\times 10x+660+20\left(5-3x\right)-130=30\left(6x+25\right)+3\times 3x\times 38$$

Multiply 6 and 10 to get 60.

$$60x+660+20\left(5-3x\right)-130=30\left(6x+25\right)+3\times 3x\times 38$$

Use the distributive property to multiply 20 by 5-3x.

$$60x+660+100-60x-130=30\left(6x+25\right)+3\times 3x\times 38$$

Add 660 and 100 to get 760.

$$60x+760-60x-130=30\left(6x+25\right)+3\times 3x\times 38$$

Combine 60x and -60x to get 0.

$$760-130=30\left(6x+25\right)+3\times 3x\times 38$$

Subtract 130 from 760 to get 630.

$$630=30\left(6x+25\right)+3\times 3x\times 38$$

Use the distributive property to multiply 30 by 6x+25.

$$630=180x+750+3\times 3x\times 38$$

Multiply 3 and 3 to get 9.

$$630=180x+750+9x\times 38$$

Multiply 9 and 38 to get 342.

$$630=180x+750+342x$$

Combine 180x and 342x to get 522x.

$$630=522x+750$$

Swap sides so that all variable terms are on the left hand side.

$$522x+750=630$$

Subtract 750 from both sides.

$$522x=630-750$$

Subtract 750 from 630 to get -120.

$$522x=-120$$

Divide both sides by 522.

$$x=\frac{-120}{522}$$

Reduce the fraction \frac{-120}{522} to lowest terms by extracting and canceling out 6.

$$x=-\frac{20}{87}$$