Answer :
Let's analyze and solve the equation [tex]\( y - 3y = 36 - 5x \)[/tex] step-by-step to find an equivalent equation:
1. Combine like terms on the left side of the equation:
The original equation is [tex]\( y - 3y = 36 - 5x \)[/tex].
Simplify the left side by combining like terms:
[tex]\[
y - 3y = -2y
\][/tex]
So the equation now is:
[tex]\[
-2y = 36 - 5x
\][/tex]
2. Solve for [tex]\( y \)[/tex]:
To isolate [tex]\( y \)[/tex], divide every term in the equation by [tex]\(-2\)[/tex]:
[tex]\[
y = \frac{36}{-2} - \frac{5x}{-2}
\][/tex]
3. Simplify each term:
Simplify [tex]\(\frac{36}{-2}\)[/tex]:
[tex]\[
\frac{36}{-2} = -18
\][/tex]
Simplify [tex]\(-\frac{5x}{-2}\)[/tex]:
[tex]\[
-\frac{5x}{-2} = \frac{5x}{2}
\][/tex]
So, substitute these values back into the equation:
[tex]\[
y = -18 + \frac{5x}{2}
\][/tex]
Rearrange the terms for clarity:
[tex]\[
y = 6 - \frac{5x}{2}
\][/tex]
Thus, the equivalent equation, after solving for [tex]\( y \)[/tex], is:
[tex]\[
y = 6 - \frac{5x}{2}
\][/tex]
1. Combine like terms on the left side of the equation:
The original equation is [tex]\( y - 3y = 36 - 5x \)[/tex].
Simplify the left side by combining like terms:
[tex]\[
y - 3y = -2y
\][/tex]
So the equation now is:
[tex]\[
-2y = 36 - 5x
\][/tex]
2. Solve for [tex]\( y \)[/tex]:
To isolate [tex]\( y \)[/tex], divide every term in the equation by [tex]\(-2\)[/tex]:
[tex]\[
y = \frac{36}{-2} - \frac{5x}{-2}
\][/tex]
3. Simplify each term:
Simplify [tex]\(\frac{36}{-2}\)[/tex]:
[tex]\[
\frac{36}{-2} = -18
\][/tex]
Simplify [tex]\(-\frac{5x}{-2}\)[/tex]:
[tex]\[
-\frac{5x}{-2} = \frac{5x}{2}
\][/tex]
So, substitute these values back into the equation:
[tex]\[
y = -18 + \frac{5x}{2}
\][/tex]
Rearrange the terms for clarity:
[tex]\[
y = 6 - \frac{5x}{2}
\][/tex]
Thus, the equivalent equation, after solving for [tex]\( y \)[/tex], is:
[tex]\[
y = 6 - \frac{5x}{2}
\][/tex]