The correct are Option A, Option C.
Step-by-step explanation:
We need to identify which expressions are equivalent.
Expressions are equivalent that are the same even though they look different.
After simplifying the expressions are same.
Checking the options:
Option A:
[tex]\frac{1}{5}x-10\,\,and\,\,\frac{1}{5}(x-50)[/tex]
The term [tex]\frac{1}{5}x-10[/tex] is in simplified form.
Simplifying [tex]\frac{1}{5}(x-50)[/tex]
[tex]\frac{1}{5}(x-50)\\Multiplying\,\,\frac{1}{5}\,\,with\,\,terms\,\,inside\,\,the\,\,bracket.\\=\frac{1}{5}x-\frac{1}{5}(50)\\=\frac{1}{5}x-10[/tex]
So, Simplifying [tex]frac{1}{5}(x-50)[/tex] we get [tex]\frac{1}{5}x-10[/tex]
Hence [tex]\frac{1}{5}x-10\,\,and\,\,\frac{1}{5}(x-50)[/tex] are equivalent.
Option A is correct.
Option B:
[tex]\frac{1}{3}x-6\,\,and\,\,-\frac{1}{3}(3x+18)[/tex]
The term [tex]\frac{1}{3}x-6[/tex] is in simplified form.
Simplifying [tex]-\frac{1}{3}(3x+18)[/tex]
[tex]-\frac{1}{3}(3x+18)\\Multiplying\,\,-\frac{1}{3}\,\,with\,\,terms\,\,inside\,\,the\,\,bracket.\\=-\frac{1}{3}*3x-\frac{1}{3}*18\\=-x-6[/tex]
Simplified form of [tex]-\frac{1}{3}(3x+18)[/tex] is: [tex]-x-6[/tex]
Since both terms are not equal so, expressions are not equivalent.
So, [tex]\frac{1}{3}x-6\,\,and\,\,-\frac{1}{3}(3x+18)[/tex] are not equivalent expression
Option B is incorrect.
Option C
[tex]\frac{1}{2}x+8\,\,and\,\,\frac{1}{2}(x+16)[/tex]
The term [tex]\frac{1}{2}x+8[/tex] is in simplified form.
Simplifying [tex]\frac{1}{2}(x+16)[/tex]
[tex]\frac{1}{2}(x+16)\\Multiplying\,\,\frac{1}{2}\,\,with\,\,terms\,\,inside\,\,the\,\,bracket\\=\frac{1}{2}*x+\frac{1}{2}*16\\=\frac{1}{2}x+8[/tex]
Since both expressions are same, both are equivalent.
Option C is correct.
Option D and Option E are not equivalent.
So, the correct are Option A, Option C.
Keywords: Solving Fractions
Learn more about Solving Fractions at:
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brainly.com/question/2456302
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