Sure, let's solve the equation [tex]\(-a - \frac{6}{7} = \frac{2}{3}\)[/tex] step-by-step to find the value of [tex]\(a\)[/tex]:
1. Starting Equation:
[tex]\[
-a - \frac{6}{7} = \frac{2}{3}
\][/tex]
2. Isolate the term involving [tex]\(a\)[/tex] by adding [tex]\(\frac{6}{7}\)[/tex] to both sides of the equation:
[tex]\[
-a = \frac{2}{3} + \frac{6}{7}
\][/tex]
3. To add the fractions [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{6}{7}\)[/tex], find a common denominator.
- The common denominator for 3 and 7 is 21.
- Rewrite each fraction with the common denominator:
[tex]\[
\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}
\][/tex]
[tex]\[
\frac{6}{7} = \frac{6 \times 3}{7 \times 3} = \frac{18}{21}
\][/tex]
4. Add the fractions:
[tex]\[
\frac{14}{21} + \frac{18}{21} = \frac{14 + 18}{21} = \frac{32}{21}
\][/tex]
5. Now, the equation is:
[tex]\[
-a = \frac{32}{21}
\][/tex]
6. Multiply both sides of the equation by -1 to solve for [tex]\(a\)[/tex]:
[tex]\[
a = -\frac{32}{21}
\][/tex]
So, the solution to the equation [tex]\(-a - \frac{6}{7} = \frac{2}{3}\)[/tex] is:
[tex]\[
a = -\frac{32}{21}
\][/tex]
Among the given multiple choice options, the correct answer is:
[tex]\[
a = -\frac{32}{21}
\][/tex]
