Solve x+21/2=4x+3/4-2-3x/8

$$x + 2 \frac { 1 } { 2 } = \frac { 4 x + 3 } { 4 } - \frac { 2 - 3 x } { 8 }$$

Solve for x

$$x = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 2,4,8.

$$8x+4\left(2\times 2+1\right)=2\left(4x+3\right)-\left(2-3x\right)$$

Multiply 2 and 2 to get 4.

$$8x+4\left(4+1\right)=2\left(4x+3\right)-\left(2-3x\right)$$

Add 4 and 1 to get 5.

$$8x+4\times 5=2\left(4x+3\right)-\left(2-3x\right)$$

Multiply 4 and 5 to get 20.

$$8x+20=2\left(4x+3\right)-\left(2-3x\right)$$

Use the distributive property to multiply 2 by 4x+3.

$$8x+20=8x+6-\left(2-3x\right)$$

To find the opposite of 2-3x, find the opposite of each term.

$$8x+20=8x+6-2-\left(-3x\right)$$

The opposite of -3x is 3x.

$$8x+20=8x+6-2+3x$$

Subtract 2 from 6 to get 4.

$$8x+20=8x+4+3x$$

Combine 8x and 3x to get 11x.

$$8x+20=11x+4$$

Subtract 11x from both sides.

$$8x+20-11x=4$$

Combine 8x and -11x to get -3x.

$$-3x+20=4$$

Subtract 20 from both sides.

$$-3x=4-20$$

Subtract 20 from 4 to get -16.

$$-3x=-16$$

Divide both sides by -3.

$$x=\frac{-16}{-3}$$

Fraction \frac{-16}{-3} can be simplified to \frac{16}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{16}{3}$$