Question

Brianna's teacher asks her which of these three expressions are equivalent to each other.

Answer 1

Answer:

Briana's thinking is incorrect because the numbers are different when you substitute x with numbers other than 0.

the two equations that are equivalent to each other are,

5x+x−4 and 9x-3x-4

Step-by-step explanation:

Expression A: 9x−3x−4

​Expression B: 12x−4

​Expression C: 5x+x−4

First I will substitute x for each of the equations.

9x-3x-4

when x equals: , then y equals:

1                        =        9(1)-3(1)-4= 2

2                       =         9(2)-3(2)-4=8

3                       =      9(3)-3(3)-4= 14

Now for 12x-4

when x equals: , then y equals:

1                        =        12(1)-4=  8

2                    =         12(2)-4= 20

3                       =      12(3)-4=  32

And for the final equation:

5x+x−4

when x equals: , then y equals:

1                        =        5(1)+(1)−4= 2

2                       =         5(2)+(2)−4 = 8

3                       =      5(3)+(3)−4=14

Based on this you can now see that the two equations that are equal are:

5x+x−4 and 9x-3x-4

~CaityConcerto

Answer 2

Answer:

Expressions A and C are equivalent.

Step-by-step explanation:

Expression A: 9x−3x−4   Combine like terms    6x -4

​Expression B: 12x−4   There are no terms to combine  12x-4

​Expression C: 5x+x−4  Combine like terms   6x -4

Brianna only looked at one particular value for x.  She must look at all values for x.