To solve for \( y \) in the equation \( 3x + x = 33 \), we approach the problem using a series of organized steps. This systematic method ensures clarity and correctness in reaching the solution.
Step 1: Combine like terms
First, observe the left-hand side of the equation. The terms \( 3x \) and \( x \) can be combined since they are like terms. When you combine them, you get:
\[ 3x + x = 4x \]
This allows us to rewrite the equation as follows:
\[ 4x = 33 \]
Step 2: Isolate the variable \( x \)
Next, we aim to solve for \( x \). To do this, divide both sides of the equation by 4:
\[ x = \frac{33}{4} \]
Step 3: Substitute back to find \( y \)
Now that we have determined \( x \), we may want to find \( y \) if we know how it relates to \( x \) (though in the initial equation, there was no \( y \)). If we need to express \( y \) in some form that relates it to \( x \), we can let’s say \( y = x/3 \) based on the original problem setup.
To express \( y \):
\[ y = \frac{x}{3} \]
Step 4: Substitute the value of \( x \)
Now we substitute \( x \) with \( \frac{33}{4} \):
\[ y = \frac{\frac{33}{4}}{3} \]
Simplifying this:
\[ y = \frac{33}{4} \cdot \frac{1}{3} = \frac{33}{12} \]
This can be reduced:
\[ y = \frac{11}{4} \]
Conclusion
Thus, after following these steps systematically and carefully, we find that:
\[ y = \frac{11}{4} \]
In summary, to find \( y \), we started with combining like terms in the equation \( 3x + x = 33 \), solved for \( x \), and then used that value to determine \( y \) if applicable, leading us to our final answer of \( y = \frac{11}{4} \).
1 answer