Question

find the value of x in the proportion. check your answer.
\\(\frac{24}{x} = \frac{6}{7}\\)

\\(x = \square\\)

Explanation:

Step1: Cross - multiply the proportion

In a proportion \(\frac{a}{b}=\frac{c}{d}\), we can cross - multiply to get \(a\times d = b\times c\). For the proportion \(\frac{24}{x}=\frac{6}{7}\), cross - multiplying gives us \(24\times7=6\times x\).
So, \(168 = 6x\).

Step2: Solve for x

To solve for \(x\), we divide both sides of the equation \(168 = 6x\) by 6.
\(x=\frac{168}{6}\)
\(x = 28\)

Step3: Check the answer

Substitute \(x = 28\) back into the original proportion.
Left - hand side: \(\frac{24}{28}=\frac{6}{7}\) (dividing numerator and denominator of \(\frac{24}{28}\) by 4 gives \(\frac{6}{7}\)).
Right - hand side: \(\frac{6}{7}\). Since left - hand side equals right - hand side, the solution is correct.

Answer:

\(28\)