Math  /  Algebra

QuestionSolve for xx : 16(x1)+x=12x=\begin{array}{l} \frac{1}{6}(x-1)+x=\frac{1}{2} \\ x=\square \end{array}

Studdy Solution
Verify the solution by substituting x=47 x = \frac{4}{7} back into the original equation:
Original equation:
16(x1)+x=12 \frac{1}{6}(x-1) + x = \frac{1}{2}
Substitute x=47 x = \frac{4}{7} :
16(471)+47 \frac{1}{6}\left(\frac{4}{7} - 1\right) + \frac{4}{7}
Calculate 471\frac{4}{7} - 1:
4777=37 \frac{4}{7} - \frac{7}{7} = -\frac{3}{7}
Substitute back:
16(37)+47=342+47 \frac{1}{6}\left(-\frac{3}{7}\right) + \frac{4}{7} = -\frac{3}{42} + \frac{4}{7}
Convert 47\frac{4}{7} to have a denominator of 42:
47=2442 \frac{4}{7} = \frac{24}{42}
Add the fractions:
342+2442=2142 -\frac{3}{42} + \frac{24}{42} = \frac{21}{42}
Simplify 2142\frac{21}{42} to 12\frac{1}{2}:
12=12 \frac{1}{2} = \frac{1}{2}
The left side equals the right side, confirming the solution is correct.
The solution is:
x=47 x = \frac{4}{7}

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