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Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solutions are correct?


He is correct because both solutions satisfy the equation.

He is not correct because he made a sign error.

He is not correct because there are no solutions.

He is not correct because there is only one solution: x = 5.



Answer :

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[tex]-2|8-x|-6=-12 \ \ \ |\hbox{add 6} \\ -2|8-x|=-6 \ \ \ |\hbox{divide by (-2)} \\ |8-x|=3 \\ 8-x=-3 \ \lor \ 8-x=3 \\ -x=-3-8 \ \lor \ -x=3-8 \\ -x=-11 \ \lor \ -x=-5 \\ x=11 \ \lor \ x=5 \\ \boxed{x=5 \hbox{ or } x=11}[/tex]

It should be x=11 instead of x=-11, so he is not correct because he made a sign error.
abidemiokin

Johan is not correct because he made a sign error. He is supposed to write 11 instead -11.

Given the moduli expression

–2|8 – x| – 6 = –12

Ths expression in moduli can either be positive and negative:

If the expression is positive, hence;

–2(8 – x) – 6 = –12

-16 + 2x - 6  = -12

2x - 22 = -12

2x = -12 + 22

2x = 10

x = 5

If the moduli is negative:

–2(-8 + x) – 6 = –12

16 - 2x - 6 = -12

-2x = -12 - 10

-2x = -22

x = 11

Hence the solution to the moduli expressions are 5 and 11.

Johan is not correct because he made a sign error. He is supposed to write 11 instead -11.

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