Sure, let's solve the given proportion step-by-step using cross multiplication.
We start with the proportion:
[tex]\[
\frac{x + 4}{3} = \frac{x + 6}{4}
\][/tex]
Step 1: Perform cross multiplication to eliminate the denominators. This involves multiplying the numerator on one side by the denominator on the other side, and vice versa. So we have:
[tex]\[
4 \cdot (x + 4) = 3 \cdot (x + 6)
\][/tex]
Step 2: Expand both sides of the equation by distributing the multiplication:
[tex]\[
4x + 16 = 3x + 18
\][/tex]
Step 3: Isolate the variable [tex]\( x \)[/tex] on one side of the equation. To do this, we'll subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[
4x - 3x + 16 = 18
\][/tex]
which simplifies to:
[tex]\[
x + 16 = 18
\][/tex]
Step 4: Solve for [tex]\( x \)[/tex] by isolating it. We do this by subtracting 16 from both sides:
[tex]\[
x + 16 - 16 = 18 - 16
\][/tex]
This simplifies to:
[tex]\[
x = 2
\][/tex]
Thus, the solution to the given proportion is:
[tex]\[
x = 2
\][/tex]
