Self Check 1.3
AlC-058-CR-003: Algebra 1, Part 2

1. Write the linear equation [tex]x = \frac{3}{2} y + \frac{9}{2}[/tex] in standard form.



Answer :

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].