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.
