To determine which expressions are equivalent after simplification, we'll simplify each expression step by step.
Expression A:
\[ -0.4b + (6b - 5.9a) \] Distributing and combining like terms: \[ 6b - 0.4b - 5.9a = 5.6b - 5.9a \]
Expression B:
\[ (3.4a - 1.7b) + (2.5a - 3.9b) \] Combining like terms: \[ 3.4a + 2.5a - 1.7b - 3.9b = (3.4 + 2.5)a + (-1.7 - 3.9)b = 5.9a - 5.6b \]
Expression C:
\[ (2.5a + 1.6b) + (3.4a + 4b) \] Combining like terms: \[ 2.5a + 3.4a + 1.6b + 4b = (2.5 + 3.4)a + (1.6 + 4)b = 5.9a + 5.6b \]
Expression D:
\[ 5.9a - 5.6b \] This is already in its simplest form.
Expression E:
\[ (-3.9b + a) + (-1.7b + 4.9a) \] Combining like terms: \[ (-3.9b - 1.7b) + (a + 4.9a) = (-3.9 - 1.7)b + (1 + 4.9)a = -5.6b + 5.9a \]
Summary of Results:
- A simplifies to \(5.6b - 5.9a\)
- B simplifies to \(5.9a - 5.6b\)
- C simplifies to \(5.9a + 5.6b\)
- D is \(5.9a - 5.6b\)
- E simplifies to \(5.9a - 5.6b\)
The equivalent expressions are:
- B: \(5.9a - 5.6b\)
- D: \(5.9a - 5.6b\)
- E: \(5.9a - 5.6b\)
So the three expressions you should check as equivalent are B, D, and E.
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