Asked by Elia Adele Marcheline on May 08, 2024
Verified
Solve ∣y8∣<8\left| \frac { y } { 8 } \right| < 88y<8 , if possible. Write the answer in set notation.
A) {y∣−8<y<8}\{ y \mid - 8 < y < 8 \}{y∣−8<y<8}
B) {y∣0<y<64}\{ y \mid 0 < y < 64 \}{y∣0<y<64}
C) {y∣−64<y<64}\{ y \mid - 64 < y < 64 \}{y∣−64<y<64}
D) {y∣−16<y<16}\{ y \mid - 16 < y < 16 \}{y∣−16<y<16}
E) no solution
Set Notation
A standardized method of describing or defining a set by clearly specifying its elements or the properties that its members must satisfy.
Absolute Value Inequality
An inequality that involves the absolute value of a variable expression and defines a range of solutions.
- Acquire the ability to solve inequalities involving absolute values.
Verified Answer
BS
Brandon StaplesMay 12, 2024
Final Answer :
C
Explanation :
To solve ∣y8∣<8\left| \frac { y } { 8 } \right| < 88y<8 , we first remove the absolute value, giving us −8<y8<8-8 < \frac{y}{8} < 8−8<8y<8 . Multiplying all parts by 8 to isolate y, we get −64<y<64-64 < y < 64−64<y<64 , which matches option C.
Learning Objectives
- Acquire the ability to solve inequalities involving absolute values.