To solve the given proportion [tex]\(\frac{3x}{5} = \frac{x+1}{2}\)[/tex], we will use the method of cross multiplication to find the value of [tex]\(x\)[/tex].
1. Cross Multiply: The basic principle of cross multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction.
[tex]\[
3x \cdot 2 = 5 \cdot (x + 1)
\][/tex]
This simplifies to:
[tex]\[
6x = 5(x + 1)
\][/tex]
2. Distribute on the Right Side: Distribute the 5 on the right side of the equation.
[tex]\[
6x = 5x + 5
\][/tex]
3. Isolate [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], subtract [tex]\(5x\)[/tex] from both sides of the equation.
[tex]\[
6x - 5x = 5
\][/tex]
4. Simplify: Now, combine like terms on the left side to simplify the equation.
[tex]\[
x = 5
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(5\)[/tex].
