Sure! To solve the equation [tex]\(\frac{8}{x}=\frac{5}{12}\)[/tex], we will follow a series of steps:
1. Understand the equation:
We are given that [tex]\(\frac{8}{x} = \frac{5}{12}\)[/tex]. This means that the ratio of [tex]\(8\)[/tex] to [tex]\(x\)[/tex] is the same as the ratio of [tex]\(5\)[/tex] to [tex]\(12\)[/tex].
2. Cross-multiplying:
To eliminate the fractions, we can use cross-multiplication. This involves multiplying the numerator of one fraction by the denominator of the other fraction and setting these equal:
[tex]\[
8 \cdot 12 = 5 \cdot x
\][/tex]
3. Perform the multiplication:
Calculate [tex]\(8 \times 12\)[/tex]:
[tex]\[
8 \times 12 = 96
\][/tex]
4. Set up the equation:
Now we have:
[tex]\[
96 = 5x
\][/tex]
5. Solve for [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], we need to isolate [tex]\(x\)[/tex] by dividing both sides of the equation by 5:
[tex]\[
x = \frac{96}{5}
\][/tex]
6. Perform the division:
Calculate [tex]\(\frac{96}{5}\)[/tex]:
[tex]\[
\frac{96}{5} = 19.2
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(19.2\)[/tex].
