Answer :

To solve the problem of finding the value of [tex]\( x \)[/tex] in the ratio [tex]\( x:6 = 3:9 \)[/tex], we can follow these steps:

1. Set up the proportion: The given ratio [tex]\( x:6 = 3:9 \)[/tex] can be expressed as a fraction. So, we write it as [tex]\(\frac{x}{6} = \frac{3}{9}\)[/tex].

2. Simplify the known ratio: The fraction [tex]\(\frac{3}{9}\)[/tex] can be simplified. Both 3 and 9 can be divided by 3, which gives [tex]\(\frac{3}{9} = \frac{1}{3}\)[/tex].

3. Rewrite the equation: Now the equation looks like [tex]\(\frac{x}{6} = \frac{1}{3}\)[/tex].

4. Cross-multiply to solve for x: To eliminate the fractions, cross-multiply:
[tex]\[
x \times 3 = 1 \times 6
\][/tex]
This results in:
[tex]\[
3x = 6
\][/tex]

5. Solve for x: Divide both sides of the equation by 3 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{6}{3} = 2
\][/tex]

Therefore, the value of [tex]\( x \)[/tex] is 2.

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Rewritten by : Barada