Enter the numbers that make the algebraic expressions equivalent.(1 point)
Expression 1: 4x+5(x−2)+?
Expression 2:
? x−11−x+9
To make the algebraic expressions equivalent, we need to find the value that should replace the "?" in each expression.
Looking at Expression 1: 4x + 5(x-2) + ?, the "?" term does not involve any variable or coefficient. Therefore, we can simply replace "?" with a constant value, let's say "a".
Expression 1: 4x + 5(x-2) + a
For Expression 2: ?x - 11 - x + 9, we have two variables, "?x" and "x". To make the expression equivalent to Expression 1, the coefficients of the "x" terms in Expression 1 and Expression 2 should be the same. In this case, the coefficient of "x" in Expression 1 is 4, so we need to make the coefficient of the "?x" term in Expression 2 also 4. This means we should replace "?" with the value of 4.
Expression 2: 4x - 11 - x + 9
So, the numbers that make the algebraic expressions equivalent are:
Expression 1: 4x + 5(x-2) + a
Expression 2: 4x - 11 - x + 9
simplify it
To simplify the expressions, we can start by expanding and combining like terms.
Expression 1: 4x + 5(x-2) + a
First, distribute the 5 to the terms inside the parentheses:
= 4x + 5x - 10 + a
Next, combine the like terms:
= 9x - 10 + a
Expression 2: 4x - 11 - x + 9
Combine the like terms:
= 3x - 2
So, the simplified expressions are:
Expression 1: 9x - 10 + a
Expression 2: 3x - 2
were the ? are at answer the question
Apologies for the confusion. To find the values that make the expressions equivalent, let's solve for the "?" in each expression.
Expression 1: 4x + 5(x-2) + ?
To solve for "?", we need more information or a specific value that the expression should be equal to.
Expression 2: ?x - 11 - x + 9
Similarly, we need more information or a specific value that the expression should be equal to in order to determine the value for "?" in Expression 2.
use the expression to answer the question
Apologies for the confusion again. Let's use the expressions to answer the question.
Expression 1: 4x + 5(x-2) + ?
Expression 2: ?x - 11 - x + 9
To make the expressions equivalent, we need the "?" in Expression 1 to be equal to the value of "4" in Expression 2.
Therefore,
Expression 1: 4x + 5(x-2) + 4
Expression 2: 4x - 11 - x + 9
Now the two expressions are equivalent.
Is 2(x−1)+18 equivalent to 6(x+3)−4x−6 ? Use algebra to find your answer. Show your work and explain your answer. (4 points)
To check if 2(x-1) + 18 is equivalent to 6(x+3) - 4x - 6, we need to simplify both expressions and see if they are equal.
Expression 1: 2(x-1) + 18
First, distribute the 2 to the terms inside the parentheses:
= 2x - 2 + 18
Next, combine like terms:
= 2x + 16
Expression 2: 6(x+3) - 4x - 6
Using the distributive property, distribute the 6 to the terms inside the parentheses:
= 6x + 18 - 4x - 6
Combine the like terms:
= (6x - 4x) + (18 - 6)
= 2x + 12
Now we can compare the simplified expressions:
Expression 1: 2x + 16
Expression 2: 2x + 12
The two expressions are not equal because they have different constant terms. Expression 1 has a constant term of +16 while Expression 2 has a constant term of +12.
Therefore, 2(x-1) + 18 is not equivalent to 6(x+3) - 4x - 6.