Question

If X/4 = x+1/5, then x =​

Answer 1

• as written, -4/15
• with parentheses, 4

Explanation:

As the problem is written, you have ...

`(x)/(4) =x+(1)/(5)\\\\5x=20x+4\qquad\text{multiply by 20}\\\\-15x=4\\\\x=-(4)/(15)`

__

If you add parentheses to include x in the numerator, then you have ...

x/4 = (x +1)/5

`5x=4(x+1)\qquad\text{multiply by 20}\\\\5x -4x = 4\qquad\text{eliminate parentheses, subtract 4x}\\\\x=4`

__

Additional comment

We include the second working because it is a fairly common mistake to neglect to put parentheses around a numerator or denominator. The solutions to such problems are not often fractions, so we suspect you intend the latter form.