Solve 3(x-3)-2(x-5)=7x+1

$$3(x-3)-2(x-5)=7x+1$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

$$3x-9-2\left(x-5\right)=7x+1$$

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

$$3x-9-2x+10=7x+1$$

Combine 3x and -2x to get x.

$$x-9+10=7x+1$$

Add -9 and 10 to get 1.

$$x+1=7x+1$$

Subtract 7x from both sides.

$$x+1-7x=1$$

Combine x and -7x to get -6x.

$$-6x+1=1$$

Subtract 1 from both sides.

$$-6x=1-1$$

Subtract 1 from 1 to get 0.

$$-6x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -6 is not equal to 0, x must be equal to 0.

$$x=0$$