Solve 3(x-2)-(x-6)=23(x-3)

$$3 ( x - 2 ) - ( x - 6 ) = 23 ( x - 3 )$$

Solve for x

$$x = \frac{23}{7} = 3\frac{2}{7} \approx 3.285714286$$

Steps for Solving Linear Equation

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

$$3x-6-\left(x-6\right)=23\left(x-3\right)$$

To find the opposite of x-6, find the opposite of each term.

$$3x-6-x-\left(-6\right)=23\left(x-3\right)$$

The opposite of -6 is 6.

$$3x-6-x+6=23\left(x-3\right)$$

Combine 3x and -x to get 2x.

$$2x-6+6=23\left(x-3\right)$$

Add -6 and 6 to get 0.

$$2x=23\left(x-3\right)$$

Use the distributive property to multiply 23 by x-3.

$$2x=23x-69$$

Subtract 23x from both sides.

$$2x-23x=-69$$

Combine 2x and -23x to get -21x.

$$-21x=-69$$

Divide both sides by -21.

$$x=\frac{-69}{-21}$$

Reduce the fraction \frac{-69}{-21} to lowest terms by extracting and canceling out -3.

$$x=\frac{23}{7}$$