Answer :
To solve the equation [tex]\(\frac{4}{x} = \frac{20}{50}\)[/tex], we want to find the value of [tex]\(x\)[/tex]. Here's how you can solve it step-by-step:
1. Understand the equation: You have a proportion where [tex]\(\frac{4}{x}\)[/tex] is equal to [tex]\(\frac{20}{50}\)[/tex].
2. Simplify the fraction on the right side: [tex]\(\frac{20}{50}\)[/tex] can be simplified by dividing both the numerator and the denominator by 10:
[tex]\[
\frac{20}{50} = \frac{2}{5}
\][/tex]
3. Set up the new equation: Now you have:
[tex]\[
\frac{4}{x} = \frac{2}{5}
\][/tex]
4. Cross-multiply: To solve for [tex]\(x\)[/tex], cross-multiply the terms:
[tex]\[
4 \times 5 = 2 \times x
\][/tex]
This gives:
[tex]\[
20 = 2x
\][/tex]
5. Solve for [tex]\(x\)[/tex]: Divide both sides of the equation by 2 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{20}{2}
\][/tex]
Simplifying further gives:
[tex]\[
x = 10
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is 10.
1. Understand the equation: You have a proportion where [tex]\(\frac{4}{x}\)[/tex] is equal to [tex]\(\frac{20}{50}\)[/tex].
2. Simplify the fraction on the right side: [tex]\(\frac{20}{50}\)[/tex] can be simplified by dividing both the numerator and the denominator by 10:
[tex]\[
\frac{20}{50} = \frac{2}{5}
\][/tex]
3. Set up the new equation: Now you have:
[tex]\[
\frac{4}{x} = \frac{2}{5}
\][/tex]
4. Cross-multiply: To solve for [tex]\(x\)[/tex], cross-multiply the terms:
[tex]\[
4 \times 5 = 2 \times x
\][/tex]
This gives:
[tex]\[
20 = 2x
\][/tex]
5. Solve for [tex]\(x\)[/tex]: Divide both sides of the equation by 2 to isolate [tex]\(x\)[/tex]:
[tex]\[
x = \frac{20}{2}
\][/tex]
Simplifying further gives:
[tex]\[
x = 10
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is 10.
