Find the solution set for the following inequality. \[ |9+2 x|>0 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choic A. The solution set is \( \{x \mid x<\square \) or \( x>\square\} \). (Type integers or simplified fractions.) B. The solution set is \( \{x \mid \square

Ask by Howell Flynn. in the United States

Feb 04,2025

To solve the inequality \( |9+2x| > 0 \), we first note that an absolute value is greater than zero when the expression inside it is not equal to zero. Therefore, we solve for when \( 9 + 2x \neq 0 \). Setting the expression equal to zero gives: \[ 9 + 2x = 0 \] \[ 2x = -9 \] \[ x = -\frac{9}{2} \] Since the absolute value is only zero at \( x = -\frac{9}{2} \), the solution set for \( |9 + 2x| > 0 \) is all real numbers except \( -\frac{9}{2} \). Thus, we can express this solution set as: C. The solution set is all real numbers except \( x = -\frac{9}{2} \), which may be formally stated as: \[ \{x \mid x < -\frac{9}{2}\} \text{ or } \{x \mid x > -\frac{9}{2}\} \] Based on this analysis, the correct answer is: A. The solution set is \( \{x \mid x < -\frac{9}{2}\} \text{ or } \{x \mid x > -\frac{9}{2}\} \).