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]
