Question

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.

Answer 1

The expressions 7x + 4 and 3x + 5 + 4x = 1 are equivalent for every value of x.

Explanation:

Expressions - 7x + 4 and 3x + 5 + 4x = 1.

1. When x = 2, both expressions have a value of 18. Let's find out:

1st expression : 7(2) + 4 = 14+4 = 18

2nd expression : 3(2) + 5 + 4(2) = 1

or 6 + 5 + 8 - 1 = 18

Values of both the expressions is 18, hence it is correct statement.

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

This is incorrect statement as we just calculated above that the expressions are equivalent for x = 2. Hence, it is incorrect.

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

Say, x = 0, then,

7x + 4 = 7 (0) + 4 = 4 and,

3x + 5 + 4x - 1 = 3(0) + 5 + 4(0) - 1 = 5-1 = 4

The statement holds.

Let's try again for x = 12,

7x + 4 = 7(12) + 4 = 88 and,

3x + 5 + 4x - 1 = 3(12) + 5 + 4(12) - 1 = 36 + 5 + 48 -1 = 88

Let's try again for x = 13,

7x + 4 = 7(13) + 4 = 95 and,

3x + 5 + 4x - 1 = 3(13) + 5 + 4(13) - 1 = 39 + 5 + 52 -1 = 95

Clearly, it holds for every value of x, whether it is odd or even. Hence, it is correct statement.

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Trick: 7x + 4 = 0....(1) and,

3x + 5 + 4x = 1

Rearranging the terms of above expression, we get,

(3x + 4x) + (5 - 1) =0

or 7x + 4 = 0...(2)

clearly both (1) & (2) are equivalent.

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