To solve the equation [tex]\(\frac{x+3}{2} = \frac{3x+5}{5}\)[/tex], one alternative method to cross multiplication is to use the multiplication property of equality. You can multiply both sides of the equation by the same number to clear the denominators.
Given the original equation:
[tex]\[
\frac{x+3}{2} = \frac{3x+5}{5}
\][/tex]
By multiplying both sides by 10, we eliminate the fractions:
[tex]\[
10 \left(\frac{x+3}{2}\right) = 10 \left(\frac{3x+5}{5}\right)
\][/tex]
Simplifying both sides:
[tex]\[
5(x+3) = 2(3x+5)
\][/tex]
Continuing with the distributive property:
[tex]\[
5x + 15 = 6x + 10
\][/tex]
Using the subtraction property of equality, subtract [tex]\(5x\)[/tex] from both sides to isolate the variable:
[tex]\[
15 = x + 10
\][/tex]
Subtracting 10 from both sides results in:
[tex]\[
5 = x
\][/tex]
Therefore, the correct method of solving this equation, other than cross multiplication, is using the multiplication property of equality to multiply both sides of the equation by 10.
