To simplify the expression [tex]\(\frac{1}{6}(30x + 24) - \frac{1}{7}(63 - 7x)\)[/tex], follow the steps in sequence:
1. Distribute [tex]\(\frac{1}{6}\)[/tex] and [tex]\(\frac{1}{7}\)[/tex]:
[tex]\[
\left(\frac{1}{6}\right)(30x) + \left(\frac{1}{6}\right)(24) - \left(\frac{1}{7}\right)(63) - \left(\frac{1}{7}\right)(-7x)
\][/tex]
2. Calculate each part:
[tex]\[
5x + 4 - 9 - (-x)
\][/tex]
3. Simplify the signs and combine like terms:
[tex]\[
5x + 4 - 9 + x
\][/tex]
4. Combine the [tex]\(x\)[/tex] terms and constants:
[tex]\[
5x + x + 4 - 9
\][/tex]
The final simplified expression is:
[tex]\[
6x - 5
\][/tex]
