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Step-by-step explanation:
Let's take the following question as an example,
[tex]\frac{2}{3} x-\frac{1}{4} = \frac{1}{6}[/tex]
Start by adding 1/4 to both sides.
[tex]\frac{2}{3} x - \frac{1}{4} + \frac{1}{4} = \frac{1}{6} + \frac{1}{4}[/tex]
[tex]\frac{2}{3}x = \frac{1}{6}+ \frac{1}{4}[/tex]
To add both 1/6 and 1/4 together we must have a common denomitor.
The common denominator for 1/6 and 1/4 is 12
[tex]\frac{2}{3}x = (\frac{1}{6}*\frac{2}{2} ) + (\frac{1}{4}*\frac{3}{3} )[/tex]
Multiple to get the common denomiators
[tex]\frac{2}{3}x = (\frac{2}{12}) + (\frac{3}{12} )[/tex]
Now we can add the fractions.
[tex]\frac{2}{3}x = \frac{5}{12}[/tex]
To get the x by itself we can either multiple by the reciprobcal of 2/3 or multiple by 3 and then divide by 2
[tex](\frac{3}{2} )* \frac{2}{3} x = (\frac{5}{12})(\frac{3}{2})[/tex]
The left side will become x as 3/2 and 2/3 cancel each other out
[tex]x = (\frac{5}{12}) (\frac{3}{2})[/tex]
Multiple the right side to get a value for x
[tex]x = \frac{15}{24}[/tex] or [tex]x = \frac{5}{8}[/tex]
If you notice we can simplfy the fraction to 5/8
