Solve 5-6x/4+x=7/2-5x-2/3

$$\frac { 5 - 6 x } { 4 } + x = \frac { 7 } { 2 } - \frac { 5 x - 2 } { 3 }$$

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 12, the least common multiple of 4,2,3.

$$3\left(5-6x\right)+12x=42-4\left(5x-2\right)$$

Use the distributive property to multiply 3 by 5-6x.

$$15-18x+12x=42-4\left(5x-2\right)$$

Combine -18x and 12x to get -6x.

$$15-6x=42-4\left(5x-2\right)$$

Use the distributive property to multiply -4 by 5x-2.

$$15-6x=42-20x+8$$

Add 42 and 8 to get 50.

$$15-6x=50-20x$$

Add 20x to both sides.

$$15-6x+20x=50$$

Combine -6x and 20x to get 14x.

$$15+14x=50$$

Subtract 15 from both sides.

$$14x=50-15$$

Subtract 15 from 50 to get 35.

$$14x=35$$

Divide both sides by 14.

$$x=\frac{35}{14}$$

Reduce the fraction \frac{35}{14} to lowest terms by extracting and canceling out 7.

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