How do is solve $\frac {12}{4}x+\frac{4}{2}=\frac {4}{2}x+\frac{12}{4}$?

Question

How does $\dfrac{12}{4}x + \dfrac{4}{2} = \dfrac{4}{2}x + \dfrac{12}{4}$ simplify to $3x + 2 = 2x + 3$ when I used an online calculator. But when I simplify the fraction, I get $4(3x+2)=4(2x+3)$. What happened to the $4$?

Answer 1

There is no difference between $12x+8=8x+12$ and $3x+2=2x+3$. Just divide the first equation by $4$ to get the second.

Answer 2

I think theer is a little confusion to whether the $x$ is in the numerator or denominator in this equation. If it's in the numerator the equation will read $$\frac {12}{4} x + \frac {4}{2} = \frac {4}{2} x + \frac {12}{4}$$ If it's in the denominator (the way I read and solved it) the equation will read $$\frac {12}{4x} + \frac {4}{2} = \frac {4}{2x} + \frac {12}{4}$$

Either way, the equations will have the same answer once we solve it.

If $x$ is in the denominator, reduce the fractions on each side to lowest terms:

$$\frac {12}{4x}+\frac{4}{2}=\frac {4}{2x}+\frac{12}{4}$$

$$\rightarrow \frac {3}{x}+2 = \frac {2}{x}+3$$

Then, multiply each side of the equation by $x$ to clear fractions:

$$3+2x=2+3x$$

Finally, subtract $2x$ and then $2$ from both sides...and you get your answer

$$x=1$$

Answer 3

12/4x + 4/2=4/2x +12/4

You can shortcut first :

3\x+2=2\x+3

Hit all the limits in x :

3+2x=2+3x

Some of the order in the equation become as follows:

3x+2=2x+3

Answer 4

There are many ways to solve such an equation.

For me, I don't like looking at fractions. So when I can clear them off the 'working slate', that is my first step.

Here, with no work out all I see that multiplying thru by $4$ is a good first step:

$\quad \frac {12}{4}x+\frac{4}{2}=\frac {4}{2}x+\frac{12}{4} \quad \text{ iff }$
$\quad \quad 4( \frac {12}{4}x+\frac{4}{2})=4(\frac {4}{2}x+\frac{12}{4}) \quad \text{ iff }$
$\quad \quad 12x +(2\times 4) = (2\times 4)x + 12 \quad \text{ iff }$
$\quad \quad 12x +8 = 8 x+ 12 \quad \text{ iff }$

We leave it to the OP to finish up from here.