Solve x-3/8+x+9/12=3x+7/20+3

$$\frac { x - 3 } { 8 } + \frac { x + 9 } { 12 } = \frac { 3 x + 7 } { 20 } + 3$$

Solve for x

$$x=51$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 120, the least common multiple of 8,12,20.

$$15\left(x-3\right)+10\left(x+9\right)=6\left(3x+7\right)+360$$

Use the distributive property to multiply 15 by x-3.

$$15x-45+10\left(x+9\right)=6\left(3x+7\right)+360$$

Use the distributive property to multiply 10 by x+9.

$$15x-45+10x+90=6\left(3x+7\right)+360$$

Combine 15x and 10x to get 25x.

$$25x-45+90=6\left(3x+7\right)+360$$

Add -45 and 90 to get 45.

$$25x+45=6\left(3x+7\right)+360$$

Use the distributive property to multiply 6 by 3x+7.

$$25x+45=18x+42+360$$

Add 42 and 360 to get 402.

$$25x+45=18x+402$$

Subtract 18x from both sides.

$$25x+45-18x=402$$

Combine 25x and -18x to get 7x.

$$7x+45=402$$

Subtract 45 from both sides.

$$7x=402-45$$

Subtract 45 from 402 to get 357.

$$7x=357$$

Divide both sides by 7.

$$x=\frac{357}{7}$$

Divide 357 by 7 to get 51.

$$x=51$$