What value of q will make the following equation true? Show all of your work or explain your answer. (You can use the E symbol to type math symbols)

Question

15(10−5q)−3=−q

Answer 1

To solve the equation \( 15(10 - 5q) - 3 = -q \), we can follow these steps:

1. Distribute the \( 15 \) on the left side of the equation: \[ 15 \times 10 - 15 \times 5q - 3 = -q \] This simplifies to: \[ 150 - 75q - 3 = -q \]

2. Combine the constant terms: \[ 150 - 3 = 147 \] So now the equation is: \[ 147 - 75q = -q \]

3. Add \( 75q \) to both sides to isolate \( q \): \[ 147 = -q + 75q \] This simplifies to: \[ 147 = 74q \]

4. Solve for \( q \) by dividing both sides by \( 74 \): \[ q = \frac{147}{74} \]

5. Simplify the fraction (if necessary). We can check if \( 147 \) and \( 74 \) have any common factors. Both \( 147 \) and \( 74 \) can be simplified:

   • \( 147 = 3 \times 49 = 3 \times 7^2 \)
   • \( 74 = 2 \times 37 \)

   There are no common factors, so \( \frac{147}{74} \) is already in its simplest form.

Thus, the final value of \( q \) is: \[ \boxed{\frac{147}{74}} \]