Questions: Problem 1.4 Solve for q. Check your solution. -2q-7=3+2q

Solution Steps

To solve for \( q \), we need to isolate the variable on one side of the equation. We can do this by adding \( 2q \) to both sides to eliminate the \( q \) term on the right side. Then, we add 7 to both sides to isolate the \( q \) term on the left side. Finally, we divide by the coefficient of \( q \) to solve for \( q \).

We start with the equation: \[ -2q - 7 = 3 + 2q \]

To isolate \( q \), we first add \( 2q \) to both sides: \[ -2q + 2q - 7 = 3 + 2q + 2q \] This simplifies to: \[ -7 = 3 + 4q \]

Next, we add 7 to both sides: \[ -7 + 7 = 3 + 4q + 7 \] This simplifies to: \[ 0 = 10 + 4q \] Now, we subtract 10 from both sides: \[ -10 = 4q \] Finally, we divide by 4: \[ q = -\frac{10}{4} = -\frac{5}{2} \]

Final Answer