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Simplify to create an equivalent expression:

[tex]6(5r - 11) - (5 - r)[/tex]

Choose one answer:

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

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

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

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

Answer :

To simplify the expression [tex]\(6(5r - 11) - (5 - r)\)[/tex], we can follow these steps:

1. Distribute the numbers outside the parentheses:
- For [tex]\(6(5r - 11)\)[/tex], distribute the 6:
[tex]\[
6 \times 5r = 30r \quad \text{and} \quad 6 \times (-11) = -66
\][/tex]
So, [tex]\(6(5r - 11)\)[/tex] becomes [tex]\(30r - 66\)[/tex].

2. Distribute the negative sign in [tex]\((-1)\)[/tex] across [tex]\((5 - r)\)[/tex]:
- Distribute the negative sign:
[tex]\[
-1 \times 5 = -5 \quad \text{and} \quad -1 \times (-r) = +r
\][/tex]
Therefore, [tex]\(-(5 - r)\)[/tex] becomes [tex]\(-5 + r\)[/tex].

3. Combine the results from both distributions:
[tex]\[
30r - 66 - 5 + r
\][/tex]

4. Combine like terms:
- Combine the terms with [tex]\(r\)[/tex]:
[tex]\[
30r + r = 31r
\][/tex]
- Combine the constant numbers:
[tex]\[
-66 - 5 = -71
\][/tex]

Now, the expression is simplified to:
[tex]\[
31r - 71
\][/tex]

Therefore, the correct answer is [tex]\((B) \, 31r - 71\)[/tex].

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