Sure, let's convert the given linear equation [tex]\( x = \frac{3}{2} y + \frac{9}{2} \)[/tex] into standard form.
### Step-by-Step Solution:
1. Starting Equation:
The given equation is:
[tex]\[
x = \frac{3}{2} y + \frac{9}{2}
\][/tex]
2. Eliminate Fractions:
To eliminate the fractions, we can multiply the entire equation by 2 (the denominator of the fractions):
[tex]\[
2 \cdot x = 2 \cdot \left( \frac{3}{2} y + \frac{9}{2} \right)
\][/tex]
This simplifies to:
[tex]\[
2x = 3y + 9
\][/tex]
3. Rearrange to Standard Form:
In standard form, a linear equation is written as [tex]\( Ax + By = C \)[/tex]. We need to get all terms involving [tex]\( x \)[/tex] and [tex]\( y \)[/tex] on one side of the equation and the constant on the other side.
Subtract [tex]\( 3y \)[/tex] from both sides to arrange the terms:
[tex]\[
2x - 3y = 9
\][/tex]
4. Result:
The equation is now in standard form.
[tex]\[
2x - 3y = 9
\][/tex]
So, the linear equation [tex]\( x = \frac{3}{2} y + \frac{9}{2} \)[/tex] in standard form is [tex]\( 2x - 3y = 9 \)[/tex].
There you go! The conversion process is now complete, and the equation [tex]\( x = \frac{3}{2} y + \frac{9}{2} \)[/tex] has successfully been rewritten in standard form as [tex]\( 2x - 3y = 9 \)[/tex].
