교과서 질문
In Exercises 59–94, solve each absolute value inequality. |3 - (2/3)x| > 5
970
views
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
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 76a
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7
검증된 단계별 안내1
Start by isolating the variable term on one side of the equation. Subtract 2x from both sides of the equation: .
Simplify the equation by combining like terms: , which simplifies to .
Next, isolate the term with the variable by subtracting 7 from both sides: .
Simplify the equation further: .
Finally, solve for by dividing both sides of the equation by 3: . After solving, determine whether the equation is an identity, a conditional equation, or an inconsistent equation based on the solution.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Types of Equations
In algebra, equations can be classified into three main types: identities, conditional equations, and inconsistent equations. An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solutions. Understanding these classifications helps in determining the nature of the solution set for any given equation.
추천 영상:
05:17
Types of Slope
Solving Linear Equations
Solving linear equations involves isolating the variable to find its value. This typically includes combining like terms, using inverse operations, and simplifying both sides of the equation. For the equation 5x + 7 = 2x + 7, one would rearrange the terms to isolate x, which is essential for determining the type of equation it represents.
추천 영상:
04:02Solving Linear Equations with Fractions
Checking Solutions
After solving an equation, it is crucial to check the solution by substituting it back into the original equation. This verification process confirms whether the solution is valid and helps identify the type of equation. For instance, if the left-hand side equals the right-hand side after substitution, it indicates whether the equation is an identity or a conditional equation.
추천 영상:
05:21Restrictions on Rational Equations
관련 실천
교과서 질문
Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).
1005
views
교과서 질문
The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|
719
views
교과서 질문
In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.
1462
views
교과서 질문
Solve each equation by the method of your choice.
883
views
교과서 질문
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 10x + 3 = 8x + 3
733
views