Question

I’m having trouble on clearing fractions. In my class, there are parentheses in the original equation. And when using distributive property, we don’t multiply the numbers within the original parentheses. Why?

Answer 1

Start with

$7\left(5x+\dfrac{1}{2}\right)=37x+\dfrac{2}{3}$

Multiply both sides by 6:

$6\cdot 7\left(5x+\dfrac{1}{2}\right)=6\left(37x+\dfrac{2}{3}\right)$

On the left hand side, we have

$6\cdot 7\left(5x+\dfrac{1}{2}\right)=42\left(5x+\dfrac{1}{2}\right)$

And we can distribute the 42 to get

$42\left(5x+\dfrac{1}{2}\right)=210x+21$

On the right hand side, we have

$6\left(37x+\dfrac{2}{3}\right)=222x+4$

So, the equation becomes

$210x+21=222x+4$

Subtract 210x from both sides to get

$21=12x+4$

Subtract 4 from both sides to get

$17=12x$

Divide both sides by 12 to get

$x=\dfrac{17}{12}$