Solve 2x+1/3-75x-2/7=x-13

$$\frac{ 2x+1 }{ 3 } -7 \frac{ 5x-2 }{ 7 } =x-13$$

Solve for x

$$x = \frac{23}{8} = 2\frac{7}{8} = 2.875$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 21, the least common multiple of 3,7.

$$7\left(2x+1\right)-21\left(5x-2\right)=21x-273$$

Use the distributive property to multiply 7 by 2x+1.

$$14x+7-21\left(5x-2\right)=21x-273$$

Use the distributive property to multiply -21 by 5x-2.

$$14x+7-105x+42=21x-273$$

Combine 14x and -105x to get -91x.

$$-91x+7+42=21x-273$$

Add 7 and 42 to get 49.

$$-91x+49=21x-273$$

Subtract 21x from both sides.

$$-91x+49-21x=-273$$

Combine -91x and -21x to get -112x.

$$-112x+49=-273$$

Subtract 49 from both sides.

$$-112x=-273-49$$

Subtract 49 from -273 to get -322.

$$-112x=-322$$

Divide both sides by -112.

$$x=\frac{-322}{-112}$$

Reduce the fraction \frac{-322}{-112} to lowest terms by extracting and canceling out -14.

$$x=\frac{23}{8}$$