High School

Which of the following is equivalent to the expression [tex]6(5r - 11) - (5 - r)[/tex]?



Choose 1 answer:

A. [tex]30r - 71[/tex]

B. [tex]31r - 71[/tex]

C. [tex]29r - 71[/tex]

D. [tex]31r - 61[/tex]

Answer :

We start with the given expression:

$$
6(5r-11)-(5-r)
$$

**Step 1. Distribute the multiplication:**
Multiply out the first term:

$$
6(5r-11) = 6 \cdot 5r - 6 \cdot 11 = 30r - 66.
$$

**Step 2. Subtract the second term:**
The expression now becomes

$$
30r - 66 - (5 - r).
$$

When subtracting a quantity in parentheses, distribute the negative sign:

$$
30r - 66 - 5 + r.
$$

**Step 3. Combine like terms:**
Combine the $r$ terms and the constants separately:

- The $r$ terms: $30r + r = 31r$.
- The constant terms: $-66 - 5 = -71$.

Thus, the simplified expression is:

$$
31r - 71.
$$

Therefore, the equivalent expression is:

$$
\boxed{31r - 71}
$$

This corresponds to option (B).