Solve c*5(x-2)+1-2x=2+3(x-2)

$$c \cdot 5 ( x - 2 ) + 1 - 2 x = 2 + 3 ( x - 2 )$$

Solve for c

$$c=-\frac{1-x}{x-2}$$

$$x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply c\times 5 by x-2.

$$5cx-2c\times 5+1-2x=2+3\left(x-2\right)$$

Multiply -2 and 5 to get -10.

$$5cx-10c+1-2x=2+3\left(x-2\right)$$

Use the distributive property to multiply 3 by x-2.

$$5cx-10c+1-2x=2+3x-6$$

Subtract 6 from 2 to get -4.

$$5cx-10c+1-2x=-4+3x$$

Subtract 1 from both sides.

$$5cx-10c-2x=-4+3x-1$$

Subtract 1 from -4 to get -5.

$$5cx-10c-2x=-5+3x$$

Add 2x to both sides.

$$5cx-10c=-5+3x+2x$$

Combine 3x and 2x to get 5x.

$$5cx-10c=-5+5x$$

Combine all terms containing c.

$$\left(5x-10\right)c=-5+5x$$

The equation is in standard form.

$$\left(5x-10\right)c=5x-5$$

Divide both sides by 5x-10.

$$\frac{\left(5x-10\right)c}{5x-10}=\frac{5x-5}{5x-10}$$

Dividing by 5x-10 undoes the multiplication by 5x-10.

$$c=\frac{5x-5}{5x-10}$$

Divide -5+5x by 5x-10.

$$c=\frac{x-1}{x-2}$$

Solve for x

$$x=-\frac{1-2c}{c-1}$$

$$c\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply c\times 5 by x-2.

$$5cx-2c\times 5+1-2x=2+3\left(x-2\right)$$

Multiply -2 and 5 to get -10.

$$5cx-10c+1-2x=2+3\left(x-2\right)$$

Use the distributive property to multiply 3 by x-2.

$$5cx-10c+1-2x=2+3x-6$$

Subtract 6 from 2 to get -4.

$$5cx-10c+1-2x=-4+3x$$

Subtract 3x from both sides.

$$5cx-10c+1-2x-3x=-4$$

Combine -2x and -3x to get -5x.

$$5cx-10c+1-5x=-4$$

Add 10c to both sides.

$$5cx+1-5x=-4+10c$$

Subtract 1 from both sides.

$$5cx-5x=-4+10c-1$$

Subtract 1 from -4 to get -5.

$$5cx-5x=-5+10c$$

Combine all terms containing x.

$$\left(5c-5\right)x=-5+10c$$

The equation is in standard form.

$$\left(5c-5\right)x=10c-5$$

Divide both sides by 5c-5.

$$\frac{\left(5c-5\right)x}{5c-5}=\frac{10c-5}{5c-5}$$

Dividing by 5c-5 undoes the multiplication by 5c-5.

$$x=\frac{10c-5}{5c-5}$$

Divide -5+10c by 5c-5.

$$x=\frac{2c-1}{c-1}$$