To solve the equation [tex]\(\frac{4}{3} b + 2 = 4 - \frac{1}{3} b\)[/tex] for [tex]\(b\)[/tex], follow these detailed steps:
1. Start with the given equation:
[tex]\[
\frac{4}{3}b + 2 = 4 - \frac{1}{3}b
\][/tex]
2. Combine the [tex]\(b\)[/tex] terms on one side of the equation. To do this, add [tex]\(\frac{1}{3}b\)[/tex] to both sides to eliminate it from the right side:
[tex]\[
\frac{4}{3}b + \frac{1}{3}b + 2 = 4
\][/tex]
3. Simplify by combining like terms:
[tex]\[
\frac{5}{3}b + 2 = 4
\][/tex]
4. Isolate the term with the variable [tex]\(b\)[/tex]. Subtract 2 from both sides of the equation:
[tex]\[
\frac{5}{3}b = 4 - 2
\][/tex]
5. Simplify the right side of the equation:
[tex]\[
\frac{5}{3}b = 2
\][/tex]
6. Solve for [tex]\(b\)[/tex] by multiplying both sides by the reciprocal of [tex]\(\frac{5}{3}\)[/tex], which is [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
b = 2 \times \frac{3}{5}
\][/tex]
7. Perform the multiplication:
[tex]\[
b = \frac{6}{5}
\][/tex]
Thus, the solution to the equation [tex]\(\frac{4}{3} b + 2 = 4 - \frac{1}{3} b\)[/tex] is
[tex]\[
b = \frac{6}{5}
\][/tex]
So, the correct answer is:
[tex]\[
b = \frac{6}{5}
\][/tex]
