To solve the problem of determining which expression is not equivalent to [tex]\(60 + 20\)[/tex], let’s evaluate each of the given expressions step-by-step.
1. Expression: [tex]\(10(6+2)\)[/tex]
- Calculate inside the parentheses first: [tex]\(6 + 2 = 8\)[/tex]
- Multiply by 10: [tex]\(10 \times 8 = 80\)[/tex]
- So, [tex]\(10(6+2) = 80\)[/tex]
2. Expression: [tex]\(5(12+4)\)[/tex]
- Calculate inside the parentheses first: [tex]\(12 + 4 = 16\)[/tex]
- Multiply by 5: [tex]\(5 \times 16 = 80\)[/tex]
- So, [tex]\(5(12+4) = 80\)[/tex]
3. Expression: [tex]\(2(30+10)\)[/tex]
- Calculate inside the parentheses first: [tex]\(30 + 10 = 40\)[/tex]
- Multiply by 2: [tex]\(2 \times 40 = 80\)[/tex]
- So, [tex]\(2(30+10) = 80\)[/tex]
4. Expression: [tex]\(10(6+1)\)[/tex]
- Calculate inside the parentheses first: [tex]\(6 + 1 = 7\)[/tex]
- Multiply by 10: [tex]\(10 \times 7 = 70\)[/tex]
- So, [tex]\(10(6+1) = 70\)[/tex]
Now, compare these results to [tex]\(60 + 20\)[/tex], which equals [tex]\(80\)[/tex].
From the evaluations:
- [tex]\(10(6+2) = 80\)[/tex]
- [tex]\(5(12+4) = 80\)[/tex]
- [tex]\(2(30+10) = 80\)[/tex]
- [tex]\(10(6+1) = 70\)[/tex]
The expression that is NOT equivalent to [tex]\(60 + 20 = 80\)[/tex] is [tex]\(10(6+1)\)[/tex], which equals [tex]\(70\)[/tex].
Therefore, the expression [tex]\(10(6+1)\)[/tex] is not equivalent to [tex]\(60+20\)[/tex]. The correct answer is:
[tex]\[ \boxed{10(6+1)} \][/tex]
