How many solutions does this equation have? $$ 4(9 q+17)=3(-7+12 q) $$

Question

UpStudy AI · Accepted Answer

Let's analyze the equation:

$$
4(9q + 17) = 3(-7 + 12q)
$$

**Step 1: Expand both sides**

$$
\begin{align*}
4(9q + 17) &= 36q + 68 \
3(-7 + 12q) &= -21 + 36q
\end{align*}
$$

**Step 2: Set the expanded forms equal to each other**

$$
36q + 68 = -21 + 36q
$$

**Step 3: Simplify the equation**

Subtract $$36q$$ from both sides:

$$
68 = -21
$$

This statement $$68 = -21$$ is clearly **false**.

**Conclusion:**

Since the equation simplifies to a false statement, there are **no solutions** to the equation.

**Answer:**  
There is no solution to the equation.
There is no solution to the equation.

How many solutions does this equation have? \( 4(9 q+17)=3(-7+12 q) \)