To determine the value of [tex]\( x \)[/tex] that satisfies the equation
[tex]\[
\frac{7}{3}\left(x+\frac{9}{28}\right)=20,
\][/tex]
follow these steps:
1. Start with the given equation:
[tex]\[
\frac{7}{3}\left(x+\frac{9}{28}\right) = 20
\][/tex]
2. Eliminate the fraction by multiplying both sides by 3/7:
[tex]\[
x + \frac{9}{28} = \left(\frac{3}{7}\right) \times 20
\][/tex]
3. Simplify the multiplication on the right-hand side:
[tex]\[
x + \frac{9}{28} = \frac{60}{7}
\][/tex]
4. Compute the value on the right-hand side:
[tex]\[
\frac{60}{7} \approx 8.571428571428571
\][/tex]
5. Isolate [tex]\( x \)[/tex] by subtracting [tex]\(\frac{9}{28}\)[/tex] from both sides:
[tex]\[
x = \left( 8.571428571428571 - \frac{9}{28} \right)
\][/tex]
6. Convert [tex]\(\frac{9}{28}\)[/tex] to a decimal to simplify the subtraction:
[tex]\[
\frac{9}{28} \approx 0.32142857142857145
\][/tex]
7. Perform the final subtraction to find [tex]\( x \)[/tex]:
[tex]\[
x = 8.571428571428571 - 0.32142857142857145
\][/tex]
8. Simplifying the subtraction yields:
[tex]\[
x = 8.25
\][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies the equation
[tex]\[
\frac{7}{3}\left(x+\frac{9}{28}\right) = 20
\][/tex]
is
[tex]\[ \boxed{8.25}. \][/tex]
