Solve {(2-x)/2+(x-1)/3}+1=4(x-2)/2

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

Solve for x

$$x = \frac{34}{13} = 2\frac{8}{13} \approx 2.615384615$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(2-x\right)+2\left(x-1\right)+6=3\times 4\left(x-2\right)$$

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

$$6-3x+2\left(x-1\right)+6=3\times 4\left(x-2\right)$$

Use the distributive property to multiply 2 by x-1.

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

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

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

Subtract 2 from 6 to get 4.

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

Add 4 and 6 to get 10.

$$10-x=3\times 4\left(x-2\right)$$

Multiply 3 and 4 to get 12.

$$10-x=12\left(x-2\right)$$

Use the distributive property to multiply 12 by x-2.

$$10-x=12x-24$$

Subtract 12x from both sides.

$$10-x-12x=-24$$

Combine -x and -12x to get -13x.

$$10-13x=-24$$

Subtract 10 from both sides.

$$-13x=-24-10$$

Subtract 10 from -24 to get -34.

$$-13x=-34$$

Divide both sides by -13.

$$x=\frac{-34}{-13}$$

Fraction \frac{-34}{-13} can be simplified to \frac{34}{13} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{34}{13}$$