To solve the rational equation [tex]\(\frac{x}{4}=\frac{9}{15}\)[/tex], we need to find the value of [tex]\(x\)[/tex] that makes both sides of the equation equal. Here is the step-by-step solution:
1. Understand the initial equation:
[tex]\[
\frac{x}{4} = \frac{9}{15}
\][/tex]
2. Cross-multiply to clear the fractions:
When you have an equation of the form [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], you can solve it by cross-multiplying. This means you multiply the numerator of each fraction by the denominator of the other fraction.
[tex]\[
x \cdot 15 = 9 \cdot 4
\][/tex]
3. Calculate the products:
- The product of [tex]\(x\)[/tex] and 15 is [tex]\(15x\)[/tex].
- The product of 9 and 4 is [tex]\(36\)[/tex].
So, we have:
[tex]\[
15x = 36
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides of the equation by 15.
[tex]\[
x = \frac{36}{15}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = 2.4
\][/tex]
Thus, the value of [tex]\(x\)[/tex] in the rational equation [tex]\(\frac{x}{4}=\frac{9}{15}\)[/tex] is [tex]\(2.4\)[/tex].
The answer is:
[tex]\[
\boxed{2.4}
\][/tex]
