Asked by Amanda Herrera on Apr 24, 2024
Verified
Solve ∣3x−24∣+6≥6\left| \frac { 3 x - 2 } { 4 } \right| + 6 \geq 643x−2+6≥6 , if possible. Write the answer in set notation.
A) {x∣x≤−23 or 23≤x}\left\{ x \mid x \leq - \frac { 2 } { 3 } \text { or } \frac { 2 } { 3 } \leq x \right\}{x∣x≤−32 or 32≤x}
B) {x∣x≤−46 or 50≤x}\{ x \mid x \leq - 46 \text { or } 50 \leq x \}{x∣x≤−46 or 50≤x}
C) {x∣−∞≤x≤∞}\{ x \mid - \infty \leq x \leq \infty \}{x∣−∞≤x≤∞}
D) {x∣23≤x}\left\{ x \mid \frac { 2 } { 3 } \leq x \right\}{x∣32≤x}
E) no solution
Set Notation
A method for specifying a set or collection of objects or numbers using brackets and symbols.
Absolute Value Inequality
An inequality that involves the absolute value of a variable expression, used to describe a range of solutions.
- Achieve an understanding of how to address absolute value inequalities.
Verified Answer
LG
Liduvina Gonzalez7 days ago
Final Answer :
C
Explanation :
The inequality simplifies to ∣3x−24∣≥0\left| \frac { 3 x - 2 } { 4 } \right| \geq 043x−2≥0 , which is always true for all real numbers because the absolute value of any real number is always greater than or equal to zero. Therefore, the solution set includes all real numbers.
Learning Objectives
- Achieve an understanding of how to address absolute value inequalities.