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2. Which value of [tex]$x$[/tex] satisfies the equation [tex]\frac{7}{3}\left(x+\frac{9}{28}\right)=20[/tex]?

A. 8.25
B. 8.89
C. 19.25
D. 44.92


Sagot :

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]