Answer:
[tex]x=\frac{2}{9}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}-x=\frac{x}{8}[/tex]
- With the equation's current format, we will have trouble solving with all these fractions. Especially the fraction [tex]\frac{x}{8}[/tex] is very difficult to deal with, so my first step would be:
[tex](\frac{8}{1})(\frac{1}{4}-x)=\frac{x}{8}(\frac{8}{1})[/tex]
- If we multiply both sides by this number, we will be able to get rid of the messy fraction on the right side as well as remove the fraction on the left side. Like so:
- I put the [tex]8[/tex] I multiplied onto each side in fraction form simply for clarity. You do not need to do this.
[tex](\frac{8}{1})(\frac{1}{4}-x)=\frac{x}{8}(\frac{8}{1})\\\frac{8}{4}-8x=\frac{8x}{8}\\2-8x=x[/tex]
- After this point, let's put our variable, [tex]x[/tex], onto one side of this equation and any other integers on the other by adding and subtracting them from both sides.
[tex]2-8x=x\\-9x=-2[/tex]
- Now we divide so that [tex]x[/tex] is isolated, and we are done.
[tex]x=\frac{-2}{-9}=\frac{2}{9}[/tex]
