James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply. 7 x + 4 and 3 x + 5 + 4 x minus 1 When x = 2, both expressions have a value of 18. The expressions are only equivalent for x = 4 and x = 6. The expressions are only equivalent when evaluated with even values. The expressions have equivalent values for any value of x. The expressions should have been evaluated with one odd value and one even value. When x = 0, the first expression has a value of 4 and the second expression has a value of 5. The expressions have equivalent values if x = 8.

Question

Mathematics

Marilyn Prince

17 November, 21:09

James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply. 7 x + 4 and 3 x + 5 + 4 x minus 1 When x = 2, both expressions have a value of 18. The expressions are only equivalent for x = 4 and x = 6. The expressions are only equivalent when evaluated with even values. The expressions have equivalent values for any value of x. The expressions should have been evaluated with one odd value and one even value. When x = 0, the first expression has a value of 4 and the second expression has a value of 5. The expressions have equivalent values if x = 8.

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Answers (1)

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Bailey Zhang · Answer 1

The following statements are true.

When x=2, both expressions have a value of 18

The expressions have equivalent values for any value of x.

The expressions have equivalent values if x = 8.

Step-by-step explanation:

The 2 given expressions are 7 x + 4 and 3 x + 5 + 4 x - 1

Statement 1:

When x = 2, both expressions have a value of 18.

The expression 7 x + 4 = 18 when x = 2

The expression 3 x + 5 + 4 x - 1 = 18 when x = 2

Hence this statement is true.

Statement 2:

The expressions are only equivalent for x = 4 and x = 6.

This statement is not true because we see that the expression is true for x = 2 also from the proof of statement 1.

Statement 3:

The expressions are only equivalent when evaluated with even values.

This statement is not true because the expressions are equivalent for odd values also. for example when x = 1 both expressions are equal to 11.

Statement 4:

The expressions have equivalent values for any value of x.

This statement is true. When we simplify the second expression 3 x + 5 + 4 x - 1, it is equal to 7 x + 4 which is the first expression. Hence it is true for all values of x.

Statement 5:

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

This statement is not true because we see that the expression is true for all values of x from statement 4.

Statement 6:

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

This statement is not true because both the expressions have value of 4 when x = 0

Statement 7:

The expressions have equivalent values if x = 8.

This statement is true because both the expressions have equivalent value for all values of x as seen in statement 4 which is true.