Question

Simplify the following expression. (5/6x+1/6)-(2/3x-1/2)

Answer 1

To simplify the expression \((\frac{5}{6}x + \frac{1}{6}) - (\frac{2}{3}x - \frac{1}{2})\), we will first remove the parentheses and ensure we correctly distribute the negative sign across the second part of the expression.

Starting with the expression:

\[
\frac{5}{6}x + \frac{1}{6} - \left(\frac{2}{3}x - \frac{1}{2}\right)
\]

Distributing the negative sign gives us:

\[
\frac{5}{6}x + \frac{1}{6} - \frac{2}{3}x + \frac{1}{2}
\]

Next, we can combine the \(x\) terms and the constant terms. First, we need a common denominator for the \(\frac{2}{3}x\) term and the constant terms \(\frac{1}{6}\) and \(\frac{1}{2}\). The common denominator for the coefficients of \(x\) is \(6\):

\[\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}\]

Now, we can substitute this into the expression:

\[
\frac{5}{6}x - \frac{4}{6}x + \frac{1}{6} + \frac{1}{2}
\]

Now, simplify the \(x\) terms:

\[
\frac{5}{6}x - \frac{4}{6}x = \frac{1}{6}x
\]

Next, we simplify the constant terms. We convert \(\frac{1}{2}\) to have a denominator of \(6\):

\[\frac{1}{2} = \frac{3}{6}\]

Now we can add the constants:

\[
\frac{1}{6} + \frac{3}{6} = \frac{4}{6}
\]

This simplifies to:

\[
\frac{4}{6} = \frac{2}{3}
\]

Putting it all together, we have:

\[
\frac{1}{6}x + \frac{2}{3}
\]

So, the simplified expression is:

\[
\frac{1}{6}x + \frac{2}{3}
\]