Solve 2(x-3)/3-4(2x-7)/6=1

$$\frac { 2 ( x - 3 ) } { 3 } - \frac { 4 ( 2 x - 7 ) } { 6 } = 1$$

Solve for x

$$x = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,6.

$$2\times 2\left(x-3\right)-4\left(2x-7\right)=6$$

Multiply 2 and 2 to get 4.

$$4\left(x-3\right)-4\left(2x-7\right)=6$$

Use the distributive property to multiply 4 by x-3.

$$4x-12-4\left(2x-7\right)=6$$

Use the distributive property to multiply -4 by 2x-7.

$$4x-12-8x+28=6$$

Combine 4x and -8x to get -4x.

$$-4x-12+28=6$$

Add -12 and 28 to get 16.

$$-4x+16=6$$

Subtract 16 from both sides.

$$-4x=6-16$$

Subtract 16 from 6 to get -10.

$$-4x=-10$$

Divide both sides by -4.

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

Reduce the fraction \frac{-10}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{5}{2}$$