Subjects algebra

Solve For W 2C1Dd9

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We are given the equation $\frac{w}{p} = \frac{2a}{b} - c$ and need to solve for $w$ step by step. 2. **Understand the equation:** The equation shows $w$ divided by $p$ equals the difference between $\frac{2a}{b}$ and $c$. 3. **Goal:** Isolate $w$ on one side to solve for it. 4. **Step 1: Write the equation clearly:** $$\frac{w}{p} = \frac{2a}{b} - c$$ 5. **Step 2: To isolate $w$, multiply both sides by $p$ to cancel the denominator on the left:** $$\cancel{p} \times \frac{w}{\cancel{p}} = p \times \left(\frac{2a}{b} - c\right)$$ which simplifies to $$w = p \left(\frac{2a}{b} - c\right)$$ 6. **Step 3: Distribute $p$ over the subtraction inside the parentheses:** $$w = p \times \frac{2a}{b} - p \times c$$ 7. **Step 4: Write the terms clearly:** $$w = \frac{2ap}{b} - pc$$ 8. **Final answer:** $$w = \frac{2ap}{b} - pc$$ This expresses $w$ in terms of $a$, $b$, $c$, and $p$. **Summary:** Multiply both sides by $p$ to clear the denominator, then distribute $p$ to each term inside the parentheses to isolate $w$.