To solve the equation [tex]\( 12x - 4y = 20 \)[/tex] for [tex]\( y \)[/tex], we will isolate [tex]\( y \)[/tex] on one side of the equation. Here is a step-by-step guide to the solution:
1. Start with the given equation:
[tex]\[
12x - 4y = 20
\][/tex]
2. Isolate the term involving [tex]\( y \)[/tex]:
To isolate [tex]\( -4y \)[/tex], we need to move the [tex]\( 12x \)[/tex] term to the right side of the equation. Subtract [tex]\( 12x \)[/tex] from both sides:
[tex]\[
-4y = 20 - 12x
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
To solve for [tex]\( y \)[/tex], we need to divide every term by [tex]\(-4\)[/tex]:
[tex]\[
y = \frac{20 - 12x}{-4}
\][/tex]
4. Simplify the expression:
We can simplify the expression by dividing both the numerator terms by [tex]\(-4\)[/tex]:
[tex]\[
y = \frac{20}{-4} - \frac{12x}{-4}
\][/tex]
[tex]\[
y = -5 + 3x
\][/tex]
5. Rewrite the expression:
Usually, we write the linear term first. Therefore, we get:
[tex]\[
y = 3x - 5
\][/tex]
So, the solution for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] is:
[tex]\[
y = 3x - 5
\][/tex]
