María determined that these expressions are equivalent expressions using the values of x = 3 and x=7. Which statements are true? Check all that apply.
5+3x-2 and x + 2(x+1)+1
The expressions are only equivalent when evaluated with odd values.
The expressions are only equivalent for x = 3 and X= 7.
The expressions should have been evaluated with one odd value and one even value.
The expressions have equivalent values when X = 6.
When x=0, the first expression has a value of 3 and the second expression has a value of 4.
The expressions have equivalent values for any value of x.
When x= 10, both expressions have a value of 33.

D, F, G / 4, 6, 7

Step-by-step explanation:

We have the following equations:

5 + 3x - 2 and x + 2(x+1) + 1

Before checking the statements. Let's solve the syste of equations:

5 + 3x - 2 = x + 2(x+1) + 1

5 + 3x - 2 = x + 2x+2 + 1

3x + 3 = 3x + 3

Both equations are equivalent. Now, let's judge the statements:

1. The expressions are only equivalent when evaluated with odd values.

Given that the both expression are the same, the expressions are equivalent for ALL values.

Therefore, the statement IS FALSE ❌

2. The expressions are only equivalent for x=3 and x=7.

Given that the both expression are the same, the expressions are equivalent for ALL values, not only x=3 and x=7.

Therefore, the statement IS FALSE ❌

3. The expressions should have been evaluated with one odd value and one even value.

If two expressions are equivalent, they should be equivalent for ALL values. Sometimes, evaluating just one odd and one even value isn't enough. That's why the best approach is to solve the system of equations.

Therefore, the statement IS FALSE ❌

4. The expressions have equivalent values when x=6.

Given that the both expression are the same, the expressions are equivalent for x=6 (And all the real values too).

Therefore, the statement IS TRUE ✅

5. When x=0, the first expression has a value of 3 and the second expression has a value of 4.

Given that BOTH expressions are equvalent, they have the same value when x=0, which is 3.

Therefore, the statement IS FALSE ❌

6. The expressions have equivalent values for any value of x.

Given that the both expression are the same, the expressions are equivalent for ALL values of x.

Therefore, the statement IS TRUE ✅

7. When x=10, both expressions have a value of 33

Given that the both expression are the same, the expressions are equivalent for ALL values of x. That's why when x=0, both expressions have a value of 33.

Therefore, the statement IS TRUE ✅

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step-by-step explanation: