Answer:
A) Brianna's thinking is incorrect because the equivalence of expressions is not solely determined by a single value of x.
B) Expressions A and C are equivalent.
C) To show which expressions are equivalent, simplify each expression by combining like terms.
Step-by-step explanation:
Given expressions:
[tex]\textsf{Expression A:}\quad 8x - 3x-4[/tex]
[tex]\textsf{Expression B:}\quad 12x-4[/tex]
[tex]\textsf{Expression C:}\quad 4x+x-4[/tex]
Brianna says that all three expressions are equivalent because the value of each one is -4 when x = 0.
Brianna's thinking is incorrect because the equivalence of expressions is not solely determined by a single value of x. To check if two expressions are equivalent, we need to confirm that they yield the same results for all possible values of x.
To determine which of the three expressions are equivalent, we can simplify each expression by combining like terms:
[tex]\textsf{Expression A:}\quad 8x - 3x-4=5x-4[/tex]
[tex]\textsf{Expression B:}\quad 12x-4[/tex]
[tex]\textsf{Expression C:}\quad 4x+x-4=5x-4[/tex]
As expression A and expression C simplify to the same result (5x - 4), then expressions A and C are equivalent.
Answer:
Brianna's thinking is incorrect because the fact that each expression evaluates to -4 when [tex] x = 0 [/tex] does not imply that the expressions are equivalent for all values of [tex] x [/tex].
Expressions A and C are equivalent
Step-by-step explanation:
Brianna's thinking is incorrect because the fact that each expression evaluates to -4 when [tex] x = 0 [/tex] does not imply that the expressions are equivalent for all values of [tex] x [/tex].
The error lies in assuming that the expressions are equivalent based solely on one value of [tex] x [/tex].
To determine which expressions are equivalent, we need to simplify each expression and compare them.
Expression A:
[tex] 8x - 3x - 4 [/tex]
[tex] = (8 - 3)x - 4 [/tex]
[tex] = 5x - 4 [/tex]
Expression B:
[tex] 12x - 4 [/tex]
Expression C:
[tex] 4x + x - 4 [/tex]
[tex] = (4 + 1)x - 4 [/tex]
[tex] = 5x - 4 [/tex]
Now, we can see that expressions A and C are equivalent because they both simplify to [tex] 5x - 4 [/tex]. Expression B is different, and it is not equivalent to expressions A and C.
In summary:
Expression A: [tex] 8x - 3x - 4 [/tex] simplifies to [tex] 5x - 4 [/tex].
Expression B: [tex] 12x - 4 [/tex] remains as [tex] 12x - 4 [/tex].
Expression C: [tex] 4x + x - 4 [/tex] simplifies to [tex] 5x - 4 [/tex].
Thus, expressions A and C are equivalent, while expression B is not equivalent to the other two.
