Sure, I'd be happy to help you solve this proportion step-by-step using cross multiplication. The given proportion is:
[tex]\[
\frac{2x + 1}{3} = \frac{x + 2}{2}
\][/tex]
Here is how you can solve it:
1. Cross multiply to eliminate the fractions:
- Multiply the numerator of the left side by the denominator of the right side.
- Multiply the numerator of the right side by the denominator of the left side.
This gives us:
[tex]\[
2 \cdot (2x + 1) = 3 \cdot (x + 2)
\][/tex]
2. Distribute both sides of the equation:
[tex]\[
2 \cdot 2x + 2 \cdot 1 = 3 \cdot x + 3 \cdot 2
\][/tex]
Which simplifies to:
[tex]\[
4x + 2 = 3x + 6
\][/tex]
3. Isolate the variable [tex]\( x \)[/tex]:
- Subtract [tex]\( 3x \)[/tex] from both sides to get all terms involving [tex]\( x \)[/tex] on one side of the equation.
[tex]\[
4x + 2 - 3x = 3x + 6 - 3x
\][/tex]
This simplifies to:
[tex]\[
x + 2 = 6
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Subtract 2 from both sides to isolate [tex]\( x \)[/tex].
[tex]\[
x + 2 - 2 = 6 - 2
\][/tex]
Which simplifies to:
[tex]\[
x = 4
\][/tex]
So, the solution to the equation is:
[tex]\[
x = 4
\][/tex]
