Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01

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Recognize that the inequality involves an absolute value expression: \(|0.01x + 1| < 0.01\). Recall that for any expression \(|A| < B\) (where \(B > 0\)), this means \(-B < A < B\).

Apply this property to the given inequality: \(-0.01 < 0.01x + 1 < 0.01\).

Next, solve the compound inequality by isolating \(x\). Start by subtracting 1 from all parts: \(-0.01 - 1 < 0.01x < 0.01 - 1\).

Simplify the inequalities: \(-1.01 < 0.01x < -0.99\).

Finally, divide all parts by \(0.01\) to solve for \(x\). Since \(0.01\) is positive, the inequality signs remain the same: \(\frac{-1.01}{0.01} < x < \frac{-0.99}{0.01}\). Express the solution set in interval notation based on these bounds.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Absolute Value Inequalities

Absolute value inequalities involve expressions where the absolute value of a variable or expression is compared to a number. To solve |A| < B, where B > 0, rewrite it as a double inequality: -B < A < B. This approach helps isolate the variable within a range.

Solving Linear Inequalities

Solving linear inequalities requires isolating the variable on one side by performing algebraic operations such as addition, subtraction, multiplication, or division. When multiplying or dividing by a negative number, the inequality sign must be reversed to maintain a true statement.

Interval Notation

Interval notation is a concise way to represent solution sets of inequalities. It uses parentheses for values not included (open intervals) and brackets for values included (closed intervals). For example, (a, b) means all numbers between a and b, excluding endpoints.