Question

Using Properties to Simplify Expressions

Instruction Active
Matching Equivalent Expressions
Match each expression on the left with an equivalent expression on the right
PLS HELP

Answer 1

1) 2x-3 = x -3 + x

2) 2x - 6 = -6 + 2x

3)
`(3)/(5)-(13)/(5)=-6.9+4.9`

4) 3x+0 = 3x

5)
`(5)/(3)-x+(1)/(3)=-(3)/(2)x+2+(1)/(2)x`

Explanation:

We need to match each expression on the left with an equivalent expression on the right

The expressions are equivalent if the have the same results.

1) 2x - 3

Looking at the options the best match is:

x -3 + x

When solve we get:

2x-3

So, 2x-3 = x -3 + x

2) 2x - 6

Looking at the options the best match is:

-6 + 2x

Because according to commutative property: a+b = b+a

So, 2x - 6 = -6 + 2x

3)
`(3)/(5)-(13)/(5)`

First simplifying the given expression:

`(3)/(5)-(13)/(5)\\=(3-13)/(5)\\=(-10)/(5)\\=-2`

Looking at the options, -6.9+4.9 = -2

So,
`(3)/(5)-(13)/(5)=-6.9+4.9`

4) 3x + 0

Looking at the options the best match is:

3x

Because, adding 0 in 3x will result in 3x

So, 3x+0 = 3x

5)
`(5)/(3)-x+(1)/(3)`

First simplifying:

`(5)/(3)-x+(1)/(3)\\=(5-3x+1)/(3)\\=(6-3x)/(3)\\= (3(2-x))/(3)\\=2-x`

Now, solving the option:
`-(3)/(2)x+2+(1)/(2)x`

`=(-3x+4+1x)/(2)\\=(-2x+4)/(2)\\=(2(-x+2))/(2)\\=-x+2\\or\\=2-x`

So,
`(5)/(3)-x+(1)/(3)=-(3)/(2)x+2+(1)/(2)x`