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Solve: [tex]-3|x-9|-10=2[/tex]

Show your work for this question.

Possible solutions:
A. [tex]\{5, -14\}[/tex]
B. No solution
C. 5
D. [tex]-13[/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\(-3|x-9|-10=2\)[/tex], let's proceed step-by-step to isolate and solve for [tex]\(x\)[/tex].

1. Isolate the absolute value term:

Start with the original equation:
[tex]\[ -3|x-9| - 10 = 2 \][/tex]

Add 10 to both sides to begin isolating the absolute value term:
[tex]\[ -3|x-9| = 12 \][/tex]

2. Divide by -3 to fully isolate the absolute value term:

[tex]\[ |x-9| = -4 \][/tex]

At this point, we notice that the absolute value of any real number (or expression) is always non-negative. Therefore, [tex]\(|x-9|\)[/tex] cannot equal [tex]\(-4\)[/tex].

3. Conclusion:

Since [tex]\(|x-9| = -4\)[/tex] is an impossible condition (no real number can have an absolute value equal to a negative number), we can conclude that there is:

No solution.

Thus, the given equation [tex]\(-3|x-9|-10=2\)[/tex] has no solution.
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