Solve 3(x+2)-10=1/4(12x-16)

$$3 ( x + 2 ) - 10 = \frac { 1 } { 4 } ( 12 x - 16 )$$

Solve for x (complex solution)

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

Solution Steps

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

$$3x+6-10=\frac{1}{4}\left(12x-16\right)$$

Subtract 10 from 6 to get -4.

$$3x-4=\frac{1}{4}\left(12x-16\right)$$

Use the distributive property to multiply \frac{1}{4} by 12x-16.

$$3x-4=\frac{1}{4}\times 12x+\frac{1}{4}\left(-16\right)$$

Multiply \frac{1}{4} and 12 to get \frac{12}{4}.

$$3x-4=\frac{12}{4}x+\frac{1}{4}\left(-16\right)$$

Divide 12 by 4 to get 3.

$$3x-4=3x+\frac{1}{4}\left(-16\right)$$

Multiply \frac{1}{4} and -16 to get \frac{-16}{4}.

$$3x-4=3x+\frac{-16}{4}$$

Divide -16 by 4 to get -4.

$$3x-4=3x-4$$

Subtract 3x from both sides.

$$3x-4-3x=-4$$

Combine 3x and -3x to get 0.

$$-4=-4$$

Compare -4 and -4.

$$\text{true}$$

This is true for any x.

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

Solve for x

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

Solution Steps

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

$$3x+6-10=\frac{1}{4}\left(12x-16\right)$$

Subtract 10 from 6 to get -4.

$$3x-4=\frac{1}{4}\left(12x-16\right)$$

Use the distributive property to multiply \frac{1}{4} by 12x-16.

$$3x-4=\frac{1}{4}\times 12x+\frac{1}{4}\left(-16\right)$$

Multiply \frac{1}{4} and 12 to get \frac{12}{4}.

$$3x-4=\frac{12}{4}x+\frac{1}{4}\left(-16\right)$$

Divide 12 by 4 to get 3.

$$3x-4=3x+\frac{1}{4}\left(-16\right)$$

Multiply \frac{1}{4} and -16 to get \frac{-16}{4}.

$$3x-4=3x+\frac{-16}{4}$$

Divide -16 by 4 to get -4.

$$3x-4=3x-4$$

Subtract 3x from both sides.

$$3x-4-3x=-4$$

Combine 3x and -3x to get 0.

$$-4=-4$$

Compare -4 and -4.

$$\text{true}$$

This is true for any x.

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