Consider the expressions 3 2 + 1 and 5 × 2 . Both are equal to 10 . That is, they are equivalent expressions.
Now let us consider some expressions that include variables, say 5 x + 2 .
The expression can be rewritten as 5 x + 2 = x + x + x + x + x + 1 + 1 .
We can re-group the right side of the equation to 2 x + 3 x + 1 + 1 or x + 4 x + 2 or some other combination. All these expressions have the same value, whenever the same value is substituted for x . That is, they are equivalent expressions.
Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Example 1:
Are the two expressions 2 y + 5 y − 5 + 8 and 7 y + 3 equivalent? Explain your answer.
Combine the like terms of the first expression.
Here, the terms 2 y and 5 y are like terms. So, add their coefficients. 2 y + 5 y = 7 y .
Also, − 5 and 8 can be combined to get 3 .
Thus, 2 y + 5 y − 5 + 8 = 7 y + 3 .
Therefore, the two expressions are equivalent.
Example 2:
Are the two expressions 6 ( 2 a + b ) and 12 a + 6 b equivalent? Explain your answer.
Use the Distributive Law to expand the first expression.
6 ( 2 a + b ) = 6 × 2 a + 6 × b = 12 a + 6 b
Therefore, the two expressions are equivalent.
Example 3:
Check whether the two expressions 2 x + 3 y and 2 y + 3 x equivalent.
The first expression is the sum of 2 x 's and 3 y 's whereas the second one is the sum of 3 x 's and 2 y 's.
Let us evaluate the expressions for some values of x and y . Take x = 0 and y = 1 .
2 ( 0 ) + 3 ( 1 ) = 0 + 3 = 3 2 ( 1 ) + 3 ( 0 ) = 2 + 0 = 2
So, there is at least one pair of values of the variables for which the two expressions are not the same.
Therefore, the two expressions are not equivalent.
Example 4:
Check whether the two expressions 3 × m × m m and m + m + m equivalent.
Consider the first expression for any non-zero values of the variable.
Cancel the common terms.
3 × m × m m = 3 m
Combine the like terms of the second expression.
m + m + m = 3 m
So, 3 × m × m m = m + m + m when m ≠ 0 .
When m = 0 , the expression 3 × m × m m is not defined.
That is, the expressions are equivalent except when m = 0 . They are not equivalent in general.
Video transcript
- Which expressions are equivalent to x plus two-y plus x plus two? Select all that apply. Alright. Let's see if I can manipulate this thing a little bit. Let me just rewrite it so I have x plus... x plus two-y plus x plus two. So, the first thing that jumps out at me, before I even look at these choices, here I have an x over here, I have an x over there. Well, if I have one x, and then I can add it to another x that would be two-x so I could rewrite this... let me do this in a different color. I could rewrite this x and this x, if I add them together that's going to be two-x. So, this is...actually, I don't want to skip any steps. So, that's x plus x plus two-y... now I'm just switching the order...plus two. And then these two x's right over here, I can just rewrite that as two-x. So, I have two-x plus two-y... plus two-y plus two. Now, let's see, out of all my choices... so, this one, this is two-x plus four-y plus four. So, that's not right, I have two-x plus two-y plus 2, so I can rule this one out. Now, this one's interesting, it looks like they have factored out a two. Let's see if we factor out a two here, what happens? So, we do see that two is a factor of that term, it's a factor of that term, and it's a factor of that term. So, let's see if we can factor it out. So, this is going to be two times x, I'll do the x in that same magenta color, two times x plus, we have just a y left when you factor out the two. And then if you factor out a two here, you're just going to have a one left. So, two times x plus y plus one. Which is exactly what they have over here. And since I was able to find a choice, I will not pick "None of the above".
Question:
What expression is equivalent to the number 28 19/100
Answers
20 + 8 + 0.1 + 0.09
Step-by-step explanation:
20 + 8 + 0.1 + 0.09
20 wholes +8 wholes =28 then...
.1 tenth+.09 hundereths=.19 add..
28+.19=. 28.19
i only know the first one 15j+15
Step-by-step explanation:
idk
Step-by-step explanation:
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