Answer :
To determine which expression is equivalent to [tex]\(8(6f + 3) - 7\)[/tex], let's simplify that expression first.
1. Simplify the Expression:
- Start with the original expression:
[tex]\[
8(6f + 3) - 7
\][/tex]
- Distribute the 8 across the terms inside the parentheses:
[tex]\[
8 \times 6f + 8 \times 3 = 48f + 24
\][/tex]
- Now, subtract 7 from the result:
[tex]\[
48f + 24 - 7 = 48f + 17
\][/tex]
Now let's check which of the options result in the same simplified expression, [tex]\(48f + 17\)[/tex].
2. Evaluate Each Option:
- Option 1: [tex]\(6f + 17\)[/tex]
- This does not match [tex]\(48f + 17\)[/tex]. Therefore, it is not equivalent.
- Option 2: [tex]\(17f + 48\)[/tex]
- This does not match [tex]\(48f + 17\)[/tex]. Therefore, it is not equivalent.
- Option 3: [tex]\(4(12f + 6) - 7\)[/tex]
- First, distribute the 4:
[tex]\[
4 \times 12f + 4 \times 6 = 48f + 24
\][/tex]
- Subtract 7 from the result:
[tex]\[
48f + 24 - 7 = 48f + 17
\][/tex]
- This matches the original simplified expression [tex]\(48f + 17\)[/tex], making it equivalent.
- Option 4: [tex]\(3(6f + 8) - 7\)[/tex]
- First, distribute the 3:
[tex]\[
3 \times 6f + 3 \times 8 = 18f + 24
\][/tex]
- Subtract 7 from the result:
[tex]\[
18f + 24 - 7 = 18f + 17
\][/tex]
- This does not match [tex]\(48f + 17\)[/tex]. Therefore, it is not equivalent.
The expression [tex]\(4(12f + 6) - 7\)[/tex] is equivalent to [tex]\(8(6f + 3) - 7\)[/tex]. Thus, the correct choice is the third option.
1. Simplify the Expression:
- Start with the original expression:
[tex]\[
8(6f + 3) - 7
\][/tex]
- Distribute the 8 across the terms inside the parentheses:
[tex]\[
8 \times 6f + 8 \times 3 = 48f + 24
\][/tex]
- Now, subtract 7 from the result:
[tex]\[
48f + 24 - 7 = 48f + 17
\][/tex]
Now let's check which of the options result in the same simplified expression, [tex]\(48f + 17\)[/tex].
2. Evaluate Each Option:
- Option 1: [tex]\(6f + 17\)[/tex]
- This does not match [tex]\(48f + 17\)[/tex]. Therefore, it is not equivalent.
- Option 2: [tex]\(17f + 48\)[/tex]
- This does not match [tex]\(48f + 17\)[/tex]. Therefore, it is not equivalent.
- Option 3: [tex]\(4(12f + 6) - 7\)[/tex]
- First, distribute the 4:
[tex]\[
4 \times 12f + 4 \times 6 = 48f + 24
\][/tex]
- Subtract 7 from the result:
[tex]\[
48f + 24 - 7 = 48f + 17
\][/tex]
- This matches the original simplified expression [tex]\(48f + 17\)[/tex], making it equivalent.
- Option 4: [tex]\(3(6f + 8) - 7\)[/tex]
- First, distribute the 3:
[tex]\[
3 \times 6f + 3 \times 8 = 18f + 24
\][/tex]
- Subtract 7 from the result:
[tex]\[
18f + 24 - 7 = 18f + 17
\][/tex]
- This does not match [tex]\(48f + 17\)[/tex]. Therefore, it is not equivalent.
The expression [tex]\(4(12f + 6) - 7\)[/tex] is equivalent to [tex]\(8(6f + 3) - 7\)[/tex]. Thus, the correct choice is the third option.
