Question

1. solve for x in the following equation: $px = r + qx$

Explanation:

Step1: Subtract \( qx \) from both sides

To isolate the terms with \( x \) on one side, we subtract \( qx \) from both sides of the equation \( px = r + qx \). This gives us \( px - qx = r + qx - qx \), which simplifies to \( px - qx = r \).

Step2: Factor out \( x \)

We can factor out \( x \) from the left - hand side of the equation \( px - qx = r \). Using the distributive property \( ax - bx=(a - b)x \), we get \( x(p - q)=r \).

Step3: Solve for \( x \)

Assuming \( p
eq q \) (so that \( p - q
eq0 \)), we divide both sides of the equation \( x(p - q)=r \) by \( p - q \). This gives us \( x=\frac{r}{p - q} \).

Answer:

\( x = \frac{r}{p - q} \) (for \( p
eq q \))