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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. 1 - Equations and Inequalities문제 61a
2장, 문제 61a

Find all values of x satisfying the given conditions. y1 = 5(2x - 8) - 2, y2 = 5(x - 3) + 3, and y1 = y2.

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1
Start by setting the two equations for y1 and y2 equal to each other, since y1 = y2. This gives the equation: 5(2x - 8) - 2 = 5(x - 3) + 3.
Distribute the 5 on both sides of the equation. For the left-hand side, distribute 5 to (2x - 8), and for the right-hand side, distribute 5 to (x - 3). This results in: 10x - 40 - 2 = 5x - 15 + 3.
Simplify both sides of the equation by combining like terms. On the left-hand side, combine -40 and -2 to get -42. On the right-hand side, combine -15 and 3 to get -12. The equation now becomes: 10x - 42 = 5x - 12.
Isolate the variable x by first eliminating the 5x term from the right-hand side. Subtract 5x from both sides: 10x - 5x - 42 = -12. This simplifies to: 5x - 42 = -12.
Solve for x by adding 42 to both sides to isolate the term with x: 5x = 30. Then divide both sides by 5 to solve for x: x = 6.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

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

Linear Equations

Linear equations are mathematical statements that express the equality of two linear expressions. They can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. Understanding how to manipulate and solve these equations is crucial for finding the values of x that satisfy the given conditions.
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Categorizing Linear Equations

Substitution Method

The substitution method involves replacing one variable with an equivalent expression from another equation. In this context, setting y1 equal to y2 allows us to create a single equation in terms of x. This method simplifies the problem and makes it easier to solve for the unknown variable.
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Choosing a Method to Solve Quadratics

Solving for x

Solving for x involves isolating the variable on one side of the equation to find its value. This process may include combining like terms, applying inverse operations, and simplifying expressions. Mastery of this concept is essential for determining the specific values of x that satisfy the equality of the two linear equations.
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