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]
