bazzy94
05.10.2019 •
Mathematics
Astudent solves the following equation for all possible values of x:
8/x+2 = 2/x-4
his solution is as follows:
step 1: 8(x – 4) = 2(x + 2)
step 2: 4(x – 4) = (x + 2)
step 3: 4x – 16 = x + 2
step 4: 3x = 18
step 5: x = 6
he determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0.
which best describes the reasonableness of the student’s solution?
a) his solution for x is correct and his explanation of the extraneous solution is reasonable.
b) his solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x.
c) his solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.
d) his solution for x is incorrect. when solved correctly, there are no extraneous solutions
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Ответ:
C) his solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.
Explanation:
To solve this rational equation, we cross multiply:
8*(x-4)=2*(x+2).
Using the distributive property, we have
8*x-8*4=2*x+2*2;
8x-32=2x+4.
Subtract 2x from each side:
8x-32-2x=2x+4-2x;
6x-32=4.
Add 32 to each side:
6x-32+32=4+32;
6x=36.
Divide both sides by 6:
x=6.
Extraneous solutions are solutions that come about in the problem but are not valid solutions to the problem; the only values of x that would give this sort of answer are -2 and 4, since these are the two values that would make one of the denominators 0 (we cannot divide by 0).
Ответ: