Problem 85 - Elementary Algebra Within Reach

Question

Use the equation and solve for \(x\). $$p_{1} x+p_{2}(a-x)=p_{3} a$$

Step-by-Step Solution

Answer

The value of \(x\) in the equation that would satisfy it is \(x = \frac{(p_{3} - p_{2})a}{(p_{1} - p_{2})}\).

Step 1: Distribute \(p_{2}\)

First, distribute \(p_{2}\) over the terms in the parenthesis (multiplication is distributable over addition). This leads to the expanded equation \(p_{1}x + p_{2}a - p_{2}x = p_{3}a\).

Step 2: Combine Similar Terms

Next, combine the similar terms on the left-hand side of the equation. \(p_{1}x - p_{2}x\) can be combined into \((p_{1} - p_{2})x\). This simplifies the equation to \((p_{1} - p_{2})x + p_{2}a = p_{3}a\).

Step 3: Isolate \(x\)

To solve for \(x\), isolate \(x\) by subtracting \(p_{2}a\) from both sides of the equation. This results in \((p_{1} - p_{2})x = p_{3}a - p_{2}a\).

Step 4: Final Calculation for \(x\)

Finally, divide both sides of the equation by \((p_{1} - p_{2})\), to isolate \(x\) on one side of the equation. This leads to the solution \(x = \frac{(p_{3} - p_{2})a}{(p_{1} - p_{2})}\)