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

$$3(x-2)+1=5(x-1)+2x$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

$$3x-6+1=5\left(x-1\right)+2x$$

Add -6 and 1 to get -5.

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

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

$$3x-5=5x-5+2x$$

Combine 5x and 2x to get 7x.

$$3x-5=7x-5$$

Subtract 7x from both sides.

$$3x-5-7x=-5$$

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

$$-4x-5=-5$$

Add 5 to both sides.

$$-4x=-5+5$$

Add -5 and 5 to get 0.

$$-4x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -4 is not equal to 0, x must be equal to 0.

$$x=0$$