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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

1 answer

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.