Answer:
The expressions 7x + 4 and 3x + 5 + 4x = 1 are equivalent for every value of x.
Step-by-step 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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