is this correct

Question

3y+x=33

Step 1: Move x to the other side by subtracting it from both sides

3y=33-x

Step 2: Divide everything by 3 to isolate y

y=33-x/3

Step 3: Simplify the fraction by dividing each term in the numerator by 3

y=11-x/3

Final answer:

The solution y= 11-x/3 is the simplest form.

Answer 1

Let's examine your steps for solving the equation \(3y + x = 33\) more carefully.

Starting with the original equation: \[ 3y + x = 33 \]

Step 1: You moved \(x\) to the other side correctly. \[ 3y = 33 - x \]

Step 2: When you divide each term by 3 to isolate \(y\), you need to be careful with how you handle the right side. The correct expression should be: \[ y = \frac{33 - x}{3} \]

Step 3: Now, you simplify the fraction. It's important to note that \(\frac{33 - x}{3}\) can indeed be separated into two terms: \[ y = \frac{33}{3} - \frac{x}{3} \] This simplifies to: \[ y = 11 - \frac{x}{3} \]

So your final answer, when simplified appropriately, should be: \[ y = 11 - \frac{x}{3} \]

Thus, the final answer \(y = 11 - \frac{x}{3}\) is correct. However, the intermediate step of \(y = 33 - x/3\) was not accurate because the division should be applied to the entire expression. Always ensure when you divide or simplify that you clearly maintain the relationship in the equation.