Question

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

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​Expression A: 9x−3x−4
​Expression B: 12x−4
​Expression C: 5x+x−4
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​Brianna says that all three expressions are equivalent because the value of each one is −4 when x=0.
​Brianna's thinking is incorrect.
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​Identify the error in Brianna's thinking.
​Determine which of the three expressions are equivalent.
​Explain or show your process in determining which expressions are equivalent.
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Enter your answers and your explanation or process in the box provided.

Answer 1

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

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

Expressions A and C are equivalent.

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.