To solve the proportion [tex]\(\frac{2}{3x} = \frac{5}{45}\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Set up the equation:
[tex]\[
\frac{2}{3x} = \frac{5}{45}
\][/tex]
2. Cross-multiply to eliminate the fractions:
[tex]\[
2 \cdot 45 = 5 \cdot 3x
\][/tex]
3. Simplify both sides:
[tex]\[
90 = 15x
\][/tex]
4. Isolate the variable [tex]\(x\)[/tex] by dividing both sides by 15:
[tex]\[
x = \frac{90}{15}
\][/tex]
5. Calculate the value of [tex]\(x\)[/tex]:
[tex]\[
x = 6
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that solves the proportion [tex]\(\frac{2}{3x} = \frac{5}{45}\)[/tex] is [tex]\(6\)[/tex].
