To solve the proportion [tex]\(\frac{x}{28} = \frac{5}{7}\)[/tex], we will use cross-multiplication. Cross-multiplying means multiplying the numerator of the first fraction by the denominator of the second fraction and setting it equal to the multiplication of the numerator of the second fraction by the denominator of the first fraction.
Here are the steps:
1. Start with the proportion:
[tex]\[
\frac{x}{28} = \frac{5}{7}
\][/tex]
2. Cross-multiply the two fractions:
[tex]\[
x \cdot 7 = 5 \cdot 28
\][/tex]
3. Simplify the right-hand side of the equation:
[tex]\[
7x = 140
\][/tex]
4. To isolate [tex]\( x \)[/tex], divide both sides of the equation by 7:
[tex]\[
x = \frac{140}{7}
\][/tex]
5. Simplify the division:
[tex]\[
x = 20
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 20 \)[/tex].
To check our answer, substitute [tex]\( x = 20 \)[/tex] back into the original proportion to verify it:
[tex]\[
\frac{20}{28} = \frac{5}{7}
\][/tex]
Simplify [tex]\(\frac{20}{28}\)[/tex] by dividing both numerator and denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{20 \div 4}{28 \div 4} = \frac{5}{7}
\][/tex]
As both sides of the original proportion are indeed equal, the solution is verified.
The solution set is [tex]\(\{ 20 \}\)[/tex].
