Consider the expressions 3 2 + 1 and 5 × 2 . Both are equal to 10 . That is, they are equivalent expressions. Show 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 Answers20 + 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: Similar Solved Works4 answers A 2,268 mm 3 B 1,134 mm 3 C 4,536 mm 3 D 3,402 mm eA 2,268 mm 3 B 1,134 mm 3 C 4,536 mm 3 D 3,402 mm e [tex]A 2,268 mm 3 B 1,134 mm 3 C 4,536 mm 3 D 3,402 mm e[/tex]... How do you find equivalent expressions?Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.
Whats a equivalent expression?Generally, if two things are the same, then it is called equivalent. Similarly, in mathematics, the equivalent expressions are the expressions that are the same, even though the expression looks different. But if the values are plugged in the expression, both the expressions give the same result.
What is an example of an equivalent expression?Examples of Equivalent Expressions
3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18. and can also be written as 6(x2 + 2y + 1) = 6x2 + 12y + 6.
Which is the equivalent to log2n 4?The correct answer is B) 16.
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What expression is equivalent to 28 and 19/100
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