Select all of the expressions that are equivalent to 4(6a + 9) - 15 - 8a

Question

responses
24a + 36 -15 - 8a
24a + 9 - 15 - 8a
24a - 8a + 36 - 15
16a + 21
24a - 6

Answer 1

Let's simplify the expression \( 4(6a + 9) - 15 - 8a \) step by step:

1. Distribute the 4: \[ 4(6a) + 4(9) = 24a + 36 \] So, the expression becomes: \[ 24a + 36 - 15 - 8a \]

2. Combine like terms: \[ 24a - 8a + 36 - 15 = (24a - 8a) + (36 - 15) \] This simplifies to: \[ 16a + 21 \]

Now we can compare this with the provided options:

1. \(24a + 36 - 15 - 8a\): Simplifying gives \(16a + 21\), which is equivalent.
2. \(24a + 9 - 15 - 8a\): Simplifying gives \(24a - 8a + 9 - 15 = 16a - 6\), which is not equivalent.
3. \(24a - 8a + 36 - 15\): Simplifying gives \(16a + 21\), which is equivalent.
4. \(16a + 21\): This is the same as the simplified result, so it is equivalent.
5. \(24a - 6\): This is not equivalent.

So the expressions that are equivalent to \(4(6a + 9) - 15 - 8a\) are:

• \(24a + 36 - 15 - 8a\)
• \(24a - 8a + 36 - 15\)
• \(16a + 21\)

In summary, the equivalent expressions are:

1. \(24a + 36 - 15 - 8a\)
2. \(24a - 8a + 36 - 15\)
3. \(16a + 21\)