Which expression is equivalent to 3 (a - 4b) - 2a + b?

Question

-a +11b

-a - 3b

5a - 3b

Answer 1

To simplify the expression \( 3(a - 4b) - 2a + b \), let's go through the steps:

1. Distribute the 3 in the first term: \[ 3(a - 4b) = 3a - 12b \]

2. Now substitute that back into the expression: \[ 3a - 12b - 2a + b \]

3. Combine like terms:

   • For the \(a\) terms: \(3a - 2a = 1a\) or just \(a\)
   • For the \(b\) terms: \(-12b + b = -11b\)

So, the simplified expression is: \[ a - 11b \]

Now, let's match this with the options provided:

• \(-a + 11b\)
• \(-a - 3b\)
• \(5a - 3b\)

None of the options match \(a - 11b\). However, \(a - 11b\) can be rewritten as \(-a + 11b\) if we negate the entire expression, but the signs here are incorrect.

Thus, the expression you provided does not seem to represent any of the options directly. However, if we correctly analyze: The equivalent expression to \(3(a - 4b) - 2a + b\) is \(a - 11b\) but appears not to match the options given.