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Answer
Step by Step Explanation
The equation given is,
[tex]\frac{1}{8}+x=\frac{1}{6}[/tex]To find the value of x.
Solution,
[tex]\begin{gathered} \frac{1}{8}+x=\frac{1}{6} \\ \mathrm{Subtract\: }\frac{1}{8}\mathrm{\: from\: both\: sides} \\ \frac{1}{8}+x-\frac{1}{8}=\frac{1}{6}-\frac{1}{8} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{1}{8}+x-\frac{1}{8} \\ =x \end{gathered}[/tex][tex]\begin{gathered} \frac{1}{6}-\frac{1}{8} \\ \text{LCM of 6 and 8 :24} \\ \text{Factor 6 = 2}\cdot3 \\ \text{Factor 8 = 2}\cdot2\cdot2 \\ \mathrm{Multiply\: each\: factor\: the\: greatest\: number\: of\: times\: it\: occurs\: in\: either\: }6\mathrm{\: or\: }8 \\ =2\cdot\: 2\cdot\: 2\cdot\: 3 \\ =24 \end{gathered}[/tex][tex]\begin{gathered} \text{Adjust the fraction based on LCM} \\ \mathrm{Multiply\: each\: numerator\: by\: the\: same\: amount\: needed\: to\: multiply\: its} \\ \mathrm{corresponding\: denominator\: to\: turn\: it\: into\: the\: LCM}\: 24 \\ \text{For 1/6 multiply denominator and numerator by 4.} \\ \frac{1}{6}=\frac{1\cdot3}{6\cdot4}=\frac{4}{24} \\ \text{For 1/8 multiply denominator and numerator by 3.} \\ \frac{1}{8}=\frac{1\cdot3}{8\cdot3}=\frac{3}{24} \end{gathered}[/tex]We Get,
[tex]\begin{gathered} =\frac{4}{24}-\frac{3}{24} \\ =\frac{4-3}{24} \\ =\frac{1}{24} \\ x=\frac{1}{24} \end{gathered}[/tex]So, the value of x is 1 / 24.
