Asked by Olivia Kerins on Jun 04, 2024
Verified
Solve ∣2x−1∣≤5| 2 x - 1 | \leq 5∣2x−1∣≤5 , if possible. Write the answer in set notation.
A) {x∣−2<x<3}\{ x \mid - 2 < x < 3 \}{x∣−2<x<3}
B) {x∣−3≤x≤2}\{ x \mid - 3 \leq x \leq 2 \}{x∣−3≤x≤2}
C) {x∣−2≤x≤3}\{ x \mid - 2 \leq x \leq 3 \}{x∣−2≤x≤3}
D) {x∣−52≤x≤52}\left\{ x \mid - \frac { 5 } { 2 } \leq x \leq \frac { 5 } { 2 } \right\}{x∣−25≤x≤25}
E) no solution
Set Notation
A system of symbols and terminology used to define and describe sets and their relationships in mathematics.
Absolute Value Inequality
An inequality that involves the absolute value of a variable or expression, comparing it to a number.
- Attain competence in addressing absolute value inequalities.
Verified Answer
CN
Chizoba NnakweJun 05, 2024
Final Answer :
C
Explanation :
To solve ∣2x−1∣≤5| 2x - 1 | \leq 5∣2x−1∣≤5 , we split it into two cases: 2x−1≤52x - 1 \leq 52x−1≤5 and 2x−1≥−52x - 1 \geq -52x−1≥−5 . Solving these gives x≤3x \leq 3x≤3 and x≥−2x \geq -2x≥−2 , respectively. Thus, the solution is {x∣−2≤x≤3}\{ x \mid - 2 \leq x \leq 3 \}{x∣−2≤x≤3} .
Learning Objectives
- Attain competence in addressing absolute value inequalities.