help/explanation

[violeta]

I have a simple problem . I have the answer but haven't got to it . can someone just show me their work? I can figure out by their example.
Here's the problem :
1/6x-2/7=4/7

thank you,
violeta

 

[soroban]

Hello, violeta!

\(\displaystyle \text{Solve for }x\!:\;\;\frac{1}{6}x - \frac{2}{7} \:=\:\frac{4}{7}\)

Multiply through by the common denominator (42):

. . \(\displaystyle 42\left(\frac{1}{6}x) - 42\left(\frac{2}{7}\right) \:=\:42\left(\frac{4}{7}\right) \quad\Rightarrow\quad 7x - 12 \:=\:24\)

. . \(\displaystyle 7x \:=\:36 \quad\Rightarrow\quad x \:=\:\dfrac{36}{7}\)