Solve x/16+2-x/4=2x/8-51/4

$$\frac { x } { 16 } + \frac { 2 - x } { 4 } = \frac { 2 x } { 8 } - 5 \frac { 1 } { 4 }$$

Solve for x

$$x = \frac{92}{7} = 13\frac{1}{7} \approx 13.142857143$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 16, the least common multiple of 16,4,8.

$$x+4\left(2-x\right)=2\times 2x-4\left(5\times 4+1\right)$$

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

$$x+8-4x=2\times 2x-4\left(5\times 4+1\right)$$

Combine x and -4x to get -3x.

$$-3x+8=2\times 2x-4\left(5\times 4+1\right)$$

Multiply 2 and 2 to get 4.

$$-3x+8=4x-4\left(5\times 4+1\right)$$

Multiply 5 and 4 to get 20.

$$-3x+8=4x-4\left(20+1\right)$$

Add 20 and 1 to get 21.

$$-3x+8=4x-4\times 21$$

Multiply -4 and 21 to get -84.

$$-3x+8=4x-84$$

Subtract 4x from both sides.

$$-3x+8-4x=-84$$

Combine -3x and -4x to get -7x.

$$-7x+8=-84$$

Subtract 8 from both sides.

$$-7x=-84-8$$

Subtract 8 from -84 to get -92.

$$-7x=-92$$

Divide both sides by -7.

$$x=\frac{-92}{-7}$$

Fraction \frac{-92}{-7} can be simplified to \frac{92}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{92}{7}$$