Question

select the expressions that are equivalent to (8r - 3) - (-r - 7). 4r + 9 -3 + r + 8r + 7 9r + 4 13r

Explanation:

Step1: Simplify the original expression

First, we need to simplify \((8r - 3)-(-r - 7)\). When we subtract a negative expression, it's equivalent to adding the positive of that expression. So we distribute the negative sign:
\((8r - 3)+(r + 7)\)

Step2: Combine like terms

Now, combine the \(r\)-terms and the constant terms. For the \(r\)-terms: \(8r+r = 9r\). For the constant terms: \(-3 + 7=4\). So the simplified expression is \(9r + 4\).

Now let's check each option:

• Option 1: \(4r + 9\) is not equal to \(9r + 4\), so this is incorrect.
• Option 2: \(-3 + r+8r + 7\). Combine like terms: \(r + 8r=9r\) and \(-3 + 7 = 4\), so this simplifies to \(9r+4\), which is correct.
• Option 3: \(9r + 4\) is exactly the simplified form of the original expression, so this is correct.
• Option 4: \(13r\) is not equal to \(9r + 4\), so this is incorrect.

Answer:

The equivalent expressions are:

• \(-3 + r + 8r + 7\)
• \(9r + 4\)