Question

Please help!! Help is def appreciated!

Answer 1

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:

$\frac{1}{5}x-10\,\,and\,\,\frac{1}{5}(x-50)$

The term $\frac{1}{5}x-10$  is in simplified form.

Simplifying $\frac{1}{5}(x-50)$

$\frac{1}{5}(x-50)\\Multiplying\,\,\frac{1}{5}\,\,with\,\,terms\,\,inside\,\,the\,\,bracket.\\=\frac{1}{5}x-\frac{1}{5}(50)\\=\frac{1}{5}x-10$

So, Simplifying $frac{1}{5}(x-50)$ we get $\frac{1}{5}x-10$

Hence $\frac{1}{5}x-10\,\,and\,\,\frac{1}{5}(x-50)$ are equivalent.

Option A is correct.

Option B:

$\frac{1}{3}x-6\,\,and\,\,-\frac{1}{3}(3x+18)$

The term $\frac{1}{3}x-6$  is in simplified form.

Simplifying $-\frac{1}{3}(3x+18)$

$-\frac{1}{3}(3x+18)\\Multiplying\,\,-\frac{1}{3}\,\,with\,\,terms\,\,inside\,\,the\,\,bracket.\\=-\frac{1}{3}*3x-\frac{1}{3}*18\\=-x-6$

Simplified form of $-\frac{1}{3}(3x+18)$ is: $-x-6$

Since both terms are not equal so, expressions are not equivalent.

So, $\frac{1}{3}x-6\,\,and\,\,-\frac{1}{3}(3x+18)$ are not equivalent expression

Option B is incorrect.

Option C

$\frac{1}{2}x+8\,\,and\,\,\frac{1}{2}(x+16)$

The term $\frac{1}{2}x+8$  is in simplified form.

Simplifying $\frac{1}{2}(x+16)$

$\frac{1}{2}(x+16)\\Multiplying\,\,\frac{1}{2}\,\,with\,\,terms\,\,inside\,\,the\,\,bracket\\=\frac{1}{2}*x+\frac{1}{2}*16\\=\frac{1}{2}x+8$

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:

• brainly.com/question/2456302
• brainly.com/question/4390083
• brainly.com/question/2456302

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