To solve the given proportion for [tex]\( x \)[/tex]:
[tex]\[
\frac{x+4}{3} = \frac{x+2}{4}
\][/tex]
we need to eliminate the denominators by cross-multiplying. This method gives us:
[tex]\[
4 \cdot (x + 4) = 3 \cdot (x + 2)
\][/tex]
Next, we expand both sides:
[tex]\[
4x + 16 = 3x + 6
\][/tex]
To isolate [tex]\( x \)[/tex], we need to get all terms involving [tex]\( x \)[/tex] on one side and the constants on the other side. We start by subtracting [tex]\( 3x \)[/tex] from both sides:
[tex]\[
4x - 3x + 16 = 3x - 3x + 6
\][/tex]
This simplifies to:
[tex]\[
x + 16 = 6
\][/tex]
Next, we subtract 16 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x + 16 - 16 = 6 - 16
\][/tex]
This simplifies to:
[tex]\[
x = -10
\][/tex]
So, the solution to the proportion is:
[tex]\[
x = -10
\][/tex]
