Solve 7(x+2)-3x-1=c(x+4)-4x+3

$$7 ( x + 2 ) - 3 x - 1 = c ( x + 4 ) - 4 x + 3$$

Solve for c

$$c=\frac{2\left(4x+5\right)}{x+4}$$

$$x\neq -4$$

Steps for Solving Linear Equation

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

$$7x+14-3x-1=c\left(x+4\right)-4x+3$$

Combine 7x and -3x to get 4x.

$$4x+14-1=c\left(x+4\right)-4x+3$$

Subtract 1 from 14 to get 13.

$$4x+13=c\left(x+4\right)-4x+3$$

Use the distributive property to multiply c by x+4.

$$4x+13=cx+4c-4x+3$$

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

$$cx+4c-4x+3=4x+13$$

Add 4x to both sides.

$$cx+4c+3=4x+13+4x$$

Combine 4x and 4x to get 8x.

$$cx+4c+3=8x+13$$

Subtract 3 from both sides.

$$cx+4c=8x+13-3$$

Subtract 3 from 13 to get 10.

$$cx+4c=8x+10$$

Combine all terms containing c.

$$\left(x+4\right)c=8x+10$$

Divide both sides by x+4.

$$\frac{\left(x+4\right)c}{x+4}=\frac{8x+10}{x+4}$$

Dividing by x+4 undoes the multiplication by x+4.

$$c=\frac{8x+10}{x+4}$$

Divide 8x+10 by x+4.

$$c=\frac{2\left(4x+5\right)}{x+4}$$

Solve for x

$$x=-\frac{2\left(5-2c\right)}{8-c}$$

$$c\neq 8$$

Steps for Solving Linear Equation

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

$$7x+14-3x-1=c\left(x+4\right)-4x+3$$

Combine 7x and -3x to get 4x.

$$4x+14-1=c\left(x+4\right)-4x+3$$

Subtract 1 from 14 to get 13.

$$4x+13=c\left(x+4\right)-4x+3$$

Use the distributive property to multiply c by x+4.

$$4x+13=cx+4c-4x+3$$

Subtract cx from both sides.

$$4x+13-cx=4c-4x+3$$

Add 4x to both sides.

$$4x+13-cx+4x=4c+3$$

Combine 4x and 4x to get 8x.

$$8x+13-cx=4c+3$$

Subtract 13 from both sides.

$$8x-cx=4c+3-13$$

Subtract 13 from 3 to get -10.

$$8x-cx=4c-10$$

Combine all terms containing x.

$$\left(8-c\right)x=4c-10$$

Divide both sides by 8-c.

$$\frac{\left(8-c\right)x}{8-c}=\frac{4c-10}{8-c}$$

Dividing by 8-c undoes the multiplication by 8-c.

$$x=\frac{4c-10}{8-c}$$

Divide 4c-10 by 8-c.

$$x=\frac{2\left(2c-5\right)}{8-c}$$