Answer :
To determine which expressions are equivalent to [tex]\(-6(-2s + 3) + 4s\)[/tex], let's simplify the given expression and compare it with the options provided.
1. Simplify the given expression:
[tex]\(-6(-2s + 3) + 4s\)[/tex]
First, distribute [tex]\(-6\)[/tex] within the parentheses:
[tex]\(-6 \times (-2s) + (-6) \times 3 + 4s\)[/tex]
This becomes:
[tex]\(12s - 18 + 4s\)[/tex]
Combine the like terms ([tex]\(12s\)[/tex] and [tex]\(4s\)[/tex]):
[tex]\(16s - 18\)[/tex]
So, the simplified form of [tex]\(-6(-2s + 3) + 4s\)[/tex] is [tex]\(16s - 18\)[/tex].
2. Compare with the given options:
- Option 1: [tex]\(16s - 18\)[/tex]
This is exactly [tex]\(16s - 18\)[/tex], which matches the simplified expression.
- Option 2: [tex]\(-6(3s - 2) + 4s\)[/tex]
Simplify this expression:
[tex]\(-6 \times 3s + (-6) \times (-2) + 4s\)[/tex]
[tex]\(-18s + 12 + 4s\)[/tex]
Combine the like terms ([tex]\(-18s\)[/tex] and [tex]\(4s\)[/tex]):
[tex]\(-14s + 12\)[/tex]
This does not match [tex]\(16s - 18\)[/tex].
- Option 3: [tex]\(2s - 18\)[/tex]
This is already simplified and is [tex]\(2s - 18\)[/tex], which does not match [tex]\(16s - 18\)[/tex].
- Option 4: [tex]\(3(-2s - 6) + 4s\)[/tex]
Simplify this expression:
[tex]\(3 \times (-2s) + 3 \times (-6) + 4s\)[/tex]
[tex]\(-6s - 18 + 4s\)[/tex]
Combine the like terms ([tex]\(-6s\)[/tex] and [tex]\(4s\)[/tex]):
[tex]\(-2s - 18\)[/tex]
This does not match [tex]\(16s - 18\)[/tex].
3. Conclusion: The expression(s) equivalent to [tex]\(-6(-2s+3)+4s\)[/tex] is:
- [tex]\(16s - 18\)[/tex] (Option 1)
1. Simplify the given expression:
[tex]\(-6(-2s + 3) + 4s\)[/tex]
First, distribute [tex]\(-6\)[/tex] within the parentheses:
[tex]\(-6 \times (-2s) + (-6) \times 3 + 4s\)[/tex]
This becomes:
[tex]\(12s - 18 + 4s\)[/tex]
Combine the like terms ([tex]\(12s\)[/tex] and [tex]\(4s\)[/tex]):
[tex]\(16s - 18\)[/tex]
So, the simplified form of [tex]\(-6(-2s + 3) + 4s\)[/tex] is [tex]\(16s - 18\)[/tex].
2. Compare with the given options:
- Option 1: [tex]\(16s - 18\)[/tex]
This is exactly [tex]\(16s - 18\)[/tex], which matches the simplified expression.
- Option 2: [tex]\(-6(3s - 2) + 4s\)[/tex]
Simplify this expression:
[tex]\(-6 \times 3s + (-6) \times (-2) + 4s\)[/tex]
[tex]\(-18s + 12 + 4s\)[/tex]
Combine the like terms ([tex]\(-18s\)[/tex] and [tex]\(4s\)[/tex]):
[tex]\(-14s + 12\)[/tex]
This does not match [tex]\(16s - 18\)[/tex].
- Option 3: [tex]\(2s - 18\)[/tex]
This is already simplified and is [tex]\(2s - 18\)[/tex], which does not match [tex]\(16s - 18\)[/tex].
- Option 4: [tex]\(3(-2s - 6) + 4s\)[/tex]
Simplify this expression:
[tex]\(3 \times (-2s) + 3 \times (-6) + 4s\)[/tex]
[tex]\(-6s - 18 + 4s\)[/tex]
Combine the like terms ([tex]\(-6s\)[/tex] and [tex]\(4s\)[/tex]):
[tex]\(-2s - 18\)[/tex]
This does not match [tex]\(16s - 18\)[/tex].
3. Conclusion: The expression(s) equivalent to [tex]\(-6(-2s+3)+4s\)[/tex] is:
- [tex]\(16s - 18\)[/tex] (Option 1)
