Question

solve the equation using any method. what is the value of x? solve for x. you can choose to show your work below or solve on paper. \\(\frac{\frac{5}{3}\left(x - \frac{9}{5}\
ight)}{\square} = \frac{7}{\square}\\) \\(x = \square\\)

Explanation:

Step1: Multiply both sides by 3

To eliminate the denominator on the left side, we multiply both sides of the equation \(\frac{\frac{5}{3}(x - \frac{9}{5})}{\square}=\frac{7}{\square}\) (assuming the denominators are 1 for simplicity as the boxes might be placeholders or typos, and the equation is \(\frac{5}{3}(x - \frac{9}{5}) = 7\)) by 3.
\(3\times\frac{5}{3}(x - \frac{9}{5})=3\times7\)
Simplifying the left side, the 3 and \(\frac{3}{1}\) cancel out: \(5(x - \frac{9}{5}) = 21\)

Step2: Distribute the 5

Using the distributive property \(a(b - c)=ab - ac\) where \(a = 5\), \(b=x\) and \(c=\frac{9}{5}\), we get:
\(5x-5\times\frac{9}{5}=21\)
Simplifying \(5\times\frac{9}{5}\) gives 9, so the equation becomes: \(5x - 9=21\)

Step3: Add 9 to both sides

To isolate the term with \(x\), we add 9 to both sides of the equation:
\(5x-9 + 9=21 + 9\)
Simplifying both sides, we have: \(5x=30\)

Step4: Divide by 5

To solve for \(x\), we divide both sides of the equation by 5:
\(\frac{5x}{5}=\frac{30}{5}\)
Simplifying, we get \(x = 6\)

Answer:

\(x = 6\)