Solve each equation or inequality. | 4.3x + 9.8| < 0

Verified step by step guidance

1. Recognize that the problem involves an absolute value inequality: \(|4.3x + 9.8| < 0\).
2. Recall the definition of absolute value: \(|A|\) represents the distance of \(A\) from zero on the number line, and it is always greater than or equal to zero.
3. Understand that \(|4.3x + 9.8|\) is always \(\geq 0\) for any real number \(x\), so the inequality \(|4.3x + 9.8| < 0\) asks when the absolute value is less than zero.
4. Since absolute values cannot be negative, there are no real values of \(x\) that satisfy \(|4.3x + 9.8| < 0\).
5. Conclude that the solution set is empty, meaning no solution exists for this inequality.

Key Concepts

Absolute Value Inequalities

Absolute value inequalities involve expressions where the absolute value of a variable or expression is compared to a number. The absolute value represents the distance from zero, so it is always non-negative. Understanding how to interpret and solve inequalities involving absolute values is essential.

Properties of Absolute Value

The absolute value of any real number is always greater than or equal to zero. This means expressions like |x| < 0 have no solution because absolute values cannot be negative. Recognizing this property helps quickly determine if an inequality has solutions.

Solving Linear Inequalities

Solving linear inequalities involves isolating the variable and determining the range of values that satisfy the inequality. When combined with absolute values, it requires considering the definition of absolute value and testing possible cases or recognizing impossible conditions.