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) 2x-3 = x -3 + x

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

3) [tex]\frac{3}{5}-\frac{13}{5}=-6.9+4.9[/tex]

4) 3x+0 = 3x

5)  [tex]\frac{5}{3}-x+\frac{1}{3}=-\frac{3}{2}x+2+\frac{1}{2}x[/tex]

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) [tex]\frac{3}{5}-\frac{13}{5}[/tex]

First simplifying the given expression:

[tex]\frac{3}{5}-\frac{13}{5}\\=\frac{3-13}{5}\\=\frac{-10}{5}\\=-2[/tex]

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

So, [tex]\frac{3}{5}-\frac{13}{5}=-6.9+4.9[/tex]

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) [tex]\frac{5}{3}-x+\frac{1}{3}[/tex]

First simplifying:

[tex]\frac{5}{3}-x+\frac{1}{3}\\=\frac{5-3x+1}{3}\\=\frac{6-3x}{3}\\= \frac{3(2-x)}{3}\\=2-x[/tex]

Now, solving the option: [tex]-\frac{3}{2}x+2+\frac{1}{2}x[/tex]

[tex]=\frac{-3x+4+1x}{2}\\=\frac{-2x+4}{2}\\=\frac{2(-x+2)}{2}\\=-x+2\\or\\=2-x[/tex]

So, [tex]\frac{5}{3}-x+\frac{1}{3}=-\frac{3}{2}x+2+\frac{1}{2}x[/tex]

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