x=\left(\frac{x+y}{3}\right)w solve for y

To solve for \( y \) in the equation:

\[
x = \left( \frac{x + y}{3} \right)w
\]

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 3 to eliminate the denominator:

\[
3x = (x + y)w
\]

### Step 2: Expand the right-hand side
Distribute \( w \) on the right-hand side:

\[
3x = xw + yw
\]

### Step 3: Move terms involving \( y \) to one side
Subtract \( xw \) from both sides to isolate terms with \( y \):

\[
3x - xw = yw
\]

### Step 4: Solve for \( y \)
Divide both sides by \( w \) to solve for \( y \):

\[
y = \frac{3x - xw}{w}
\]

This is the expression for \( y \).

Would you like more details or have any questions? Here are five related problems to try:

1. Solve \( x = \frac{x - y}{4} + 2 \) for \( y \).
2. Solve \( y = \frac{3x + y}{2} - w \) for \( y \).
3. Solve \( x = \left( \frac{2x + 3y}{5} \right)z \) for \( y \).
4. Solve \( z = \left( \frac{y + z}{6} \right)x \) for \( y \).
5. Solve \( x = \left( \frac{x + 2y}{4} \right)w + 1 \) for \( y \).

**Tip**: When solving equations with fractions, multiplying both sides by the denominator is often a good first step to simplify.

x = \left(\frac{x + y}{3}\right)w solve for y

Learn how to solve for y in the equation x = (x + y)/3 * w with a step-by-step explanation. This algebraic problem involves fraction elimination and linear equation solving, suitable for students in Grades 9-11.

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