Sure! Let's solve the equation [tex]\( x + 3y = 6 \)[/tex] for [tex]\( y \)[/tex].
### Step-by-step Solution:
1. Start with the given equation:
[tex]\[
x + 3y = 6
\][/tex]
2. Isolate the [tex]\( y \)[/tex]-term on one side of the equation:
To do this, we'll subtract [tex]\( x \)[/tex] from both sides of the equation:
[tex]\[
3y = 6 - x
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
Now, we want to isolate [tex]\( y \)[/tex] completely, so we need to divide both sides of the equation by 3:
[tex]\[
y = \frac{6 - x}{3}
\][/tex]
4. Simplify the expression:
We can split the fraction into two separate terms:
[tex]\[
y = \frac{6}{3} - \frac{x}{3}
\][/tex]
5. Reduce the fractions:
Simplify each term:
[tex]\[
y = 2 - \frac{x}{3}
\][/tex]
So, the solution for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[
y = 2 - \frac{x}{3}
\][/tex]
This is the simplified form of the equation, and it tells you how [tex]\( y \)[/tex] depends on [tex]\( x \)[/tex].
