Solve 3x/4-16+7x/20=2(x-2)/5

$$\frac { 3 x } { 4 } - \frac { 16 + 7 x } { 20 } = \frac { 2 ( x - 2 ) } { 5 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,20,5.

$$5\times 3x-\left(16+7x\right)=4\times 2\left(x-2\right)$$

Multiply 5 and 3 to get 15.

$$15x-\left(16+7x\right)=4\times 2\left(x-2\right)$$

To find the opposite of 16+7x, find the opposite of each term.

$$15x-16-7x=4\times 2\left(x-2\right)$$

Combine 15x and -7x to get 8x.

$$8x-16=4\times 2\left(x-2\right)$$

Multiply 4 and 2 to get 8.

$$8x-16=8\left(x-2\right)$$

Use the distributive property to multiply 8 by x-2.

$$8x-16=8x-16$$

Subtract 8x from both sides.

$$8x-16-8x=-16$$

Combine 8x and -8x to get 0.

$$-16=-16$$

Compare -16 and -16.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by 20, the least common multiple of 4,20,5.

$$5\times 3x-\left(16+7x\right)=4\times 2\left(x-2\right)$$

Multiply 5 and 3 to get 15.

$$15x-\left(16+7x\right)=4\times 2\left(x-2\right)$$

To find the opposite of 16+7x, find the opposite of each term.

$$15x-16-7x=4\times 2\left(x-2\right)$$

Combine 15x and -7x to get 8x.

$$8x-16=4\times 2\left(x-2\right)$$

Multiply 4 and 2 to get 8.

$$8x-16=8\left(x-2\right)$$

Use the distributive property to multiply 8 by x-2.

$$8x-16=8x-16$$

Subtract 8x from both sides.

$$8x-16-8x=-16$$

Combine 8x and -8x to get 0.

$$-16=-16$$

Compare -16 and -16.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$