9514 1404 393
Answer:
A. some values (x = 4)
B. all values
C. no values
Step-by-step explanation:
If you subtract the right-side expression from both sides of an equation, so you get something of the form ...
f(x) = 0
Then there are three possibilities:
f(x) is some function of x . . . . "some values" make it true*
f(x) = 0 . . . . "all values" make it true; the equation is an identity
f(x) = constant (non-zero) . . . . "no values" of x will make it true
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A: 3x = x +8
3x -(x +8) = 0
2x -8 = 0 . . . . . . . . true for "some" values of x, namely, x = 4
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B: 5x -(x +x +x +x +x) = 0
0 = 0 . . . . . . . . . . . true for "all" values of x
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C: 2(x +5) -(2x +5) = 0
2x + 10 -2x -5 = 0
5 = 0 . . . . . . . . . . . true for "no values" of x (always FALSE)
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* The possibility exists that the function f(x) does not have 0 in its range. In that case, there are no real solutions for the equation. For example |x|+1 = 0 has no solutions. For expressions linear in x, there will always be a solution.
