To solve the equation [tex]\(2(3a - 4) - 3(a + 1) = 4\)[/tex], we'll go step-by-step:
1. Distribute the constants inside the parentheses:
For the term [tex]\(2(3a - 4)\)[/tex]:
[tex]\[
2 \times 3a - 2 \times 4 = 6a - 8
\][/tex]
For the term [tex]\(-3(a + 1)\)[/tex]:
[tex]\[
-3 \times a - 3 \times 1 = -3a - 3
\][/tex]
So, the equation now looks like:
[tex]\[
6a - 8 - 3a - 3 = 4
\][/tex]
2. Combine like terms:
Combine the terms involving [tex]\(a\)[/tex]:
[tex]\[
6a - 3a = 3a
\][/tex]
Combine the constant terms:
[tex]\[
-8 - 3 = -11
\][/tex]
This reduces our equation to:
[tex]\[
3a - 11 = 4
\][/tex]
3. Isolate the variable [tex]\(a\)[/tex]:
Add 11 to both sides of the equation to move the constant term to the right side:
[tex]\[
3a - 11 + 11 = 4 + 11
\][/tex]
Simplify:
[tex]\[
3a = 15
\][/tex]
4. Solve for [tex]\(a\)[/tex]:
Divide both sides by 3 to isolate [tex]\(a\)[/tex]:
[tex]\[
a = \frac{15}{3}
\][/tex]
Simplify:
[tex]\[
a = 5
\][/tex]
Therefore, the solution to the equation [tex]\(2(3a - 4) - 3(a + 1) = 4\)[/tex] is [tex]\(a = 5\)[/tex].
Among the given options, the correct answer is:
a. [tex]\(a = 5\)[/tex]
