Answered

IDNLearn.com is designed to help you find accurate answers with ease. Join our knowledgeable community and get detailed, reliable answers to all your questions.

Solve the inequality:

[tex]\[ 5 - 3|6 - x| \ \textless \ 11 \][/tex]

Sagot :

GinnyAnsweridn
Let's solve the inequality [tex]\( 5 - 3|6 - x| < 11 \)[/tex] step-by-step:

1. Isolate the absolute value term:
- Start with the given inequality: [tex]\( 5 - 3|6 - x| < 11 \)[/tex].
- Subtract 5 from both sides to isolate the absolute value term:
[tex]\[ -3|6 - x| < 6 \][/tex]

2. Divide both sides by -3:
- When dividing by a negative number, the direction of the inequality reverses. So:
[tex]\[ |6 - x| > -2 \][/tex]

3. Analyze the inequality [tex]\( |6 - x| > -2 \)[/tex]:
- The absolute value [tex]\( |6 - x| \)[/tex] represents a non-negative quantity (it is always greater than or equal to 0).
- Since the right side of the inequality is -2, which is negative, [tex]\( |6 - x| \)[/tex] will always be greater than -2 for any real number [tex]\( x \)[/tex].

4. Conclusion:
- Because an absolute value cannot be negative and thus is always greater than any negative number, the inequality [tex]\( |6 - x| > -2 \)[/tex] is always true for all real numbers [tex]\( x \)[/tex].

Therefore, the inequality [tex]\( 5 - 3|6 - x| < 11 \)[/tex] holds for all real numbers [tex]\( x \)[/tex].
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.