Question

Using Properties to Simplify Expressions

Answer 1

Answer:

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

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

3) $\frac{3}{5}-\frac{13}{5}=-6.9+4.9$

4) 3x+0 = 3x

5)  $\frac{5}{3}-x+\frac{1}{3}=-\frac{3}{2}x+2+\frac{1}{2}x$

Step-by-step 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) $\frac{3}{5}-\frac{13}{5}$

First simplifying the given expression:

$\frac{3}{5}-\frac{13}{5}\\=\frac{3-13}{5}\\=\frac{-10}{5}\\=-2$

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

So, $\frac{3}{5}-\frac{13}{5}=-6.9+4.9$

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) $\frac{5}{3}-x+\frac{1}{3}$

First simplifying:

$\frac{5}{3}-x+\frac{1}{3}\\=\frac{5-3x+1}{3}\\=\frac{6-3x}{3}\\= \frac{3(2-x)}{3}\\=2-x$

Now, solving the option: $-\frac{3}{2}x+2+\frac{1}{2}x$

$=\frac{-3x+4+1x}{2}\\=\frac{-2x+4}{2}\\=\frac{2(-x+2)}{2}\\=-x+2\\or\\=2-x$

So, $\frac{5}{3}-x+\frac{1}{3}=-\frac{3}{2}x+2+\frac{1}{2}x$