교과서 질문
Write each complex number in standard form. (2 + 3i)3
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
2장, 문제 64
In Exercises 59–94, solve each absolute value inequality. |3x + 5| < 17
검증된 단계별 안내1
Recall that an absolute value inequality of the form \(|A| < B\) (where \(B > 0\)) can be rewritten as a compound inequality: \(-B < A < B\).
Apply this rule to the given inequality \(|3x + 5| < 17\), which becomes \(-17 < 3x + 5 < 17\).
Next, solve the compound inequality by isolating \(x\). Start by subtracting 5 from all parts: \(-17 - 5 < 3x < 17 - 5\).
Simplify the inequalities: \(-22 < 3x < 12\).
Finally, divide all parts by 3 to solve for \(x\): \(\frac{-22}{3} < x < 4\).
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Absolute Value Definition
The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For any expression |A|, it equals A if A is non-negative, and -A if A is negative. Understanding this helps in rewriting absolute value inequalities into equivalent compound inequalities.
추천 영상:
08:07
Vertex Form
Solving Absolute Value Inequalities
An inequality of the form |A| < B (where B > 0) can be rewritten as a compound inequality: -B < A < B. This means the expression inside the absolute value lies between -B and B. This approach allows solving the inequality by breaking it into two linear inequalities.
추천 영상:
06:07Linear Inequalities
Linear Inequalities
Once the absolute value inequality is rewritten without absolute values, it becomes a linear inequality or a system of inequalities. Solving these involves isolating the variable using algebraic operations like addition, subtraction, multiplication, or division, while considering the direction of the inequality.
추천 영상:
06:07Linear Inequalities
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