To solve the proportion [tex]\(\frac{x+4}{3} = \frac{x+6}{4}\)[/tex] using cross multiplication, follow these steps:
1. Set up the cross multiplication: Cross multiply the terms to eliminate the fractions: [tex]\[
4(x + 4) = 3(x + 6)
\][/tex]
2. Distribute the terms: Multiply each side by the respective numerators: [tex]\[
4x + 16 = 3x + 18
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]: To isolate [tex]\(x\)[/tex], start by getting all the terms involving [tex]\(x\)[/tex] on one side of the equation and the constant terms on the other side. Subtract [tex]\(3x\)[/tex] from both sides: [tex]\[
4x - 3x + 16 = 18
\][/tex] Simplify: [tex]\[
x + 16 = 18
\][/tex]
4. Solve for [tex]\(x\)[/tex]: Subtract 16 from both sides to solve for [tex]\(x\)[/tex]: [tex]\[
x = 18 - 16
\][/tex] Simplify: [tex]\[
x = 2
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the proportion is: [tex]\[
x = 2
\][/tex]
