Simplify: 3(a - 4) + 2(2a + 5)

Simplify: 3(a - 4) + 2(2a + 5)

• A. 5a + 2
• B. 4a - 6
• C. 7a - 2
• D. 7a + 2

Answer: (C)

Distributing and combining like terms is the key idea here. First, apply the distributive property to each part: 3(a − 4) becomes 3a − 12, and 2(2a + 5) becomes 4a + 10. Now you have 3a − 12 + 4a + 10. Combine like terms: 3a and 4a add to 7a, while −12 and +10 add to −2. Put it together, and the expression simplifies to 7a − 2. This matches the correct simplified form. If you test with a value for a, it checks out (for example, a = 1 gives 5 both in the original and in the simplified form).

Distributing and combining like terms is the key idea here. First, apply the distributive property to each part: 3(a − 4) becomes 3a − 12, and 2(2a + 5) becomes 4a + 10. Now you have 3a − 12 + 4a + 10. Combine like terms: 3a and 4a add to 7a, while −12 and +10 add to −2. Put it together, and the expression simplifies to 7a − 2. This matches the correct simplified form. If you test with a value for a, it checks out (for example, a = 1 gives 5 both in the original and in the simplified form).