Asked by Garrett Spain on Jul 22, 2024
Verified
Solve ∣a+8∣2≥20\frac { | a + 8 | } { 2 } \geq 202∣a+8∣≥20 , if possible. Write the answer in set notation.
A) {a∣a≤−48 or a≥32}\{ a \mid a \leq - 48 \text { or } a \geq 32 \}{a∣a≤−48 or a≥32}
B) {a∣a≤−96 or a≥64}\{ a \mid a \leq - 96 \text { or } a \geq 64 \}{a∣a≤−96 or a≥64}
C) {a∣−48≤a≤32}\{ a \mid - 48 \leq a \leq 32 \}{a∣−48≤a≤32}
D) {a∣−96≤a≤64}\{ a \mid - 96 \leq a \leq 64 \}{a∣−96≤a≤64}
E) no solution
Set Notation
A symbolic way of representing and specifying a set and its elements using curly brackets and specific symbols.
Absolute Value Inequality
An inequality that contains an absolute value expression, setting constraints on the range of solutions.
- Learn to effectively solve inequalities associated with absolute values.
Verified Answer
RK
Rubab Khalid
Jul 26, 2024
Final Answer :
A
Explanation :
To solve ∣a+8∣2≥20\frac { | a + 8 | } { 2 } \geq 202∣a+8∣≥20 , multiply both sides by 2 to get ∣a+8∣≥40| a + 8 | \geq 40∣a+8∣≥40 . This inequality means a+8≥40a + 8 \geq 40a+8≥40 or a+8≤−40a + 8 \leq -40a+8≤−40 . Solving these gives a≥32a \geq 32a≥32 or a≤−48a \leq -48a≤−48 , which matches option A.
Learning Objectives
- Learn to effectively solve inequalities associated with absolute values.