Answer :
Sure! Let's simplify the expression step by step:
Given expression:
[tex]\[ 6(5r - 11) - (5 - r) \][/tex]
1. Distribute the 6 in the first term:
Multiply 6 with each term inside the parentheses:
[tex]\[ 6 \times 5r = 30r \][/tex]
[tex]\[ 6 \times (-11) = -66 \][/tex]
So, the first part becomes:
[tex]\[ 30r - 66 \][/tex]
2. Distribute the minus sign in the second term:
Distribute the negative sign across the terms in the parentheses:
[tex]\[ -(5) = -5 \][/tex]
[tex]\[ -(-r) = +r \][/tex]
So, the second part becomes:
[tex]\[ -5 + r \][/tex]
3. Combine like terms:
Now, combine all terms:
[tex]\[ (30r - 66) + (-5 + r) \][/tex]
Combine the 'r' terms:
[tex]\[ 30r + r = 31r \][/tex]
Combine the constant terms:
[tex]\[ -66 - 5 = -71 \][/tex]
So, the simplified expression is:
[tex]\[ 31r - 71 \][/tex]
Therefore, the equivalent expression to [tex]\[ 6(5r - 11) - (5 - r) \][/tex] is [tex]\[ 31r - 71 \][/tex].
The correct answer choice is (B) [tex]\( 31r - 71 \)[/tex].
Given expression:
[tex]\[ 6(5r - 11) - (5 - r) \][/tex]
1. Distribute the 6 in the first term:
Multiply 6 with each term inside the parentheses:
[tex]\[ 6 \times 5r = 30r \][/tex]
[tex]\[ 6 \times (-11) = -66 \][/tex]
So, the first part becomes:
[tex]\[ 30r - 66 \][/tex]
2. Distribute the minus sign in the second term:
Distribute the negative sign across the terms in the parentheses:
[tex]\[ -(5) = -5 \][/tex]
[tex]\[ -(-r) = +r \][/tex]
So, the second part becomes:
[tex]\[ -5 + r \][/tex]
3. Combine like terms:
Now, combine all terms:
[tex]\[ (30r - 66) + (-5 + r) \][/tex]
Combine the 'r' terms:
[tex]\[ 30r + r = 31r \][/tex]
Combine the constant terms:
[tex]\[ -66 - 5 = -71 \][/tex]
So, the simplified expression is:
[tex]\[ 31r - 71 \][/tex]
Therefore, the equivalent expression to [tex]\[ 6(5r - 11) - (5 - r) \][/tex] is [tex]\[ 31r - 71 \][/tex].
The correct answer choice is (B) [tex]\( 31r - 71 \)[/tex].
