Question

Which of the following expressions has a simplified value of 3a+2?
-10-5a+12+8a
-a+4+51-a-6
-6a+9a+4-2
-8+3a+10-a

Answer 1

To determine which of the given expressions simplifies to \(3a + 2\), let's simplify each one step by step.

1. **First expression:**
\[
-10 - 5a + 12 + 8a
\]
Combine like terms:
\[
(-5a + 8a) + (-10 + 12) = 3a + 2
\]

2. **Second expression:**
\[
-a + 4 + 51 - a - 6
\]
Combine like terms:
\[
(-a - a) + (4 + 51 - 6) = -2a + 49
\]

3. **Third expression:**
\[
-6a + 9a + 4 - 2
\]
Combine like terms:
\[
(-6a + 9a) + (4 - 2) = 3a + 2
\]

4. **Fourth expression:**
\[
-8 + 3a + 10 - a
\]
Combine like terms:
\[
(3a - a) + (-8 + 10) = 2a + 2
\]

Now, we can summarize the results:
- The first expression simplifies to \(3a + 2\).
- The second expression simplifies to \(-2a + 49\).
- The third expression simplifies to \(3a + 2\).
- The fourth expression simplifies to \(2a + 2\).

Thus, the expressions that simplify to \(3a + 2\) are:
- **First expression:** \(-10 - 5a + 12 + 8a\)
- **Third expression:** \(-6a + 9a + 4 - 2\)

Therefore, the answer is **the first expression and the third expression.**