Solve 3(x+2x+1/3)-(x-2x+1/3)=5(2x-2x+1/3)+37

$$3(x+ \frac{ 2x+1 }{ 3 } )-(x- \frac{ 2x+1 }{ 3 } )=5(2x- \frac{ 2x+1 }{ 3 } )+37$$

Solve for x

$$x=-17$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$9\left(x+\frac{2x+1}{3}\right)-3\left(x-\frac{2x+1}{3}\right)=15\left(2x-\frac{2x+1}{3}\right)+111$$

Use the distributive property to multiply 9 by x+\frac{2x+1}{3}.

$$9x+9\times \frac{2x+1}{3}-3\left(x-\frac{2x+1}{3}\right)=15\left(2x-\frac{2x+1}{3}\right)+111$$

Cancel out 3, the greatest common factor in 9 and 3.

$$9x+3\left(2x+1\right)-3\left(x-\frac{2x+1}{3}\right)=15\left(2x-\frac{2x+1}{3}\right)+111$$

Use the distributive property to multiply 3 by 2x+1.

$$9x+6x+3-3\left(x-\frac{2x+1}{3}\right)=15\left(2x-\frac{2x+1}{3}\right)+111$$

Combine 9x and 6x to get 15x.

$$15x+3-3\left(x-\frac{2x+1}{3}\right)=15\left(2x-\frac{2x+1}{3}\right)+111$$

Use the distributive property to multiply 15 by 2x-\frac{2x+1}{3}.

$$15x+3-3\left(x-\frac{2x+1}{3}\right)=30x+15\left(-\frac{2x+1}{3}\right)+111$$

Cancel out 3, the greatest common factor in 15 and 3.

$$15x+3-3\left(x-\frac{2x+1}{3}\right)=30x-5\left(2x+1\right)+111$$

Use the distributive property to multiply -5 by 2x+1.

$$15x+3-3\left(x-\frac{2x+1}{3}\right)=30x-10x-5+111$$

Combine 30x and -10x to get 20x.

$$15x+3-3\left(x-\frac{2x+1}{3}\right)=20x-5+111$$

Add -5 and 111 to get 106.

$$15x+3-3\left(x-\frac{2x+1}{3}\right)=20x+106$$

Divide each term of 2x+1 by 3 to get \frac{2}{3}x+\frac{1}{3}.

$$15x+3-3\left(x-\left(\frac{2}{3}x+\frac{1}{3}\right)\right)=20x+106$$

To find the opposite of \frac{2}{3}x+\frac{1}{3}, find the opposite of each term.

$$15x+3-3\left(x-\frac{2}{3}x-\frac{1}{3}\right)=20x+106$$

Combine x and -\frac{2}{3}x to get \frac{1}{3}x.

$$15x+3-3\left(\frac{1}{3}x-\frac{1}{3}\right)=20x+106$$

Use the distributive property to multiply -3 by \frac{1}{3}x-\frac{1}{3}.

$$15x+3-3\times \frac{1}{3}x-3\left(-\frac{1}{3}\right)=20x+106$$

Multiply -3 times \frac{1}{3}.

$$15x+3-x-3\left(-\frac{1}{3}\right)=20x+106$$

Multiply -3 times -\frac{1}{3}.

$$15x+3-x+1=20x+106$$

Combine 15x and -x to get 14x.

$$14x+3+1=20x+106$$

Add 3 and 1 to get 4.

$$14x+4=20x+106$$

Subtract 20x from both sides.

$$14x+4-20x=106$$

Combine 14x and -20x to get -6x.

$$-6x+4=106$$

Subtract 4 from both sides.

$$-6x=106-4$$

Subtract 4 from 106 to get 102.

$$-6x=102$$

Divide both sides by -6.

$$x=\frac{102}{-6}$$

Divide 102 by -6 to get -17.

$$x=-17$$