Question

Which pair shows equivalent expressions?
213x+2) - 23x+1
O 243x+2) = 5x+4
o 213x+4)=x+2
0 23x+4) = 2£x+8
2.

Answer 1

Given:

The pair of expressions in the options.

To find:

The pair that shows equivalent expressions.

Solution:

We have,

$2\left(\dfrac{2}{5}x+2\right)$

By using distributive property, we get

$2\left(\dfrac{2}{5}x+2\right)=2\left(\dfrac{2}{5}x\right)+2(2)$

$2\left(\dfrac{2}{5}x+2\right)=\dfrac{4}{5}x+4$

So, option A is incorrect and option B is correct.

We have,

$2\left(\dfrac{2}{5}x+4\right)$

By using distributive property, we get

$2\left(\dfrac{2}{5}x+4\right)=2\left(\dfrac{2}{5}x\right)+2(4)$

$2\left(\dfrac{2}{5}x+4\right)=\dfrac{4}{5}x+8$

So, options C and D both are incorrect.

Therefore, the correct option is B.

Answer 2

The correct pair of equivalents expressions is B.

Multiplication of expressions

To solve the question, one must have knowledge about the multiplication of expressions.

When you have an expression being multiplied by a value, you multiply all the terms of the expression by that value, so that:

                                     $a (x + y) = ax + ay$

Thus, performing this multiplication for all alternatives we have:

a) $2 (\frac{2}{5}x + 2) = \frac{4}{5}x + 4$

b) $2 (\frac{2}{5}x + 2) = \frac{4}{5}x + 4$

c) $2 (\frac{2}{5}x + 4) = \frac{4}{5}x + 8$

d) $2 (\frac{2}{5}x + 2) = \frac{4}{5}x + 8$

So, the only expression that correctly corresponds to the answer is that of alternative B.

Learn more about expressions in: brainly.com/question/439355