https://file.aiquickdraw.com/mathbot/file/172774414214105bvrc03.jpg

The equation shown in the image is:

\[
-4q + 10 = -8 + 2q
\]

Let's solve it to determine how many solutions it has.

### Step 1: Simplify both sides.
The equation is already simplified on both sides:

Left-hand side: \(-4q + 10\)  
Right-hand side: \(-8 + 2q\)

### Step 2: Move all terms involving \(q\) to one side.
To do this, subtract \(2q\) from both sides:

\[
-4q - 2q + 10 = -8
\]
\[
-6q + 10 = -8
\]

### Step 3: Move constant terms to the other side.
Subtract 10 from both sides:

\[
-6q = -8 - 10
\]
\[
-6q = -18
\]

### Step 4: Solve for \(q\).
Divide both sides by \(-6\):

\[
q = \frac{-18}{-6} = 3
\]

### Conclusion:
There is exactly **one solution**, which is \(q = 3\).

### Answer: **One solution**

Would you like more details or have any questions?

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Here are 5 related questions you might consider:
1. How do you solve equations with variables on both sides?
2. What is the meaning of "no solution" in an equation?
3. Can there be infinitely many solutions to a linear equation?
4. How do you check if your solution is correct after solving an equation?
5. What happens if the variables cancel out and you're left with a true statement?

**Tip**: When solving equations, always check your work by substituting your solution back into the original equation.

How many solutions does the equation -4q + 10 = -8 + 2q have?

Learn how to solve the equation -4q + 10 = -8 + 2q step by step. This algebra problem focuses on solving linear equations with variables on both sides. Suitable for students in Grade 8.

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