Textbook Question
In Exercises 67–70, find all values of x such that y = 0.
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
Chapter 2, Problem 68a
In Exercises 67–70, find all values of x such that y = 0.
y = 2[3x - (4x - 6)] - 5(x - 6)
Verified step by step guidance1
Start by simplifying the expression for y. Distribute the 2 across the terms inside the brackets: y = 2[3x - (4x - 6)] becomes y = 2[3x - 4x + 6].
Simplify the terms inside the brackets: y = 2[-x + 6]. Then distribute the 2 to each term: y = -2x + 12.
Now simplify the second part of the equation, -5(x - 6). Distribute the -5: y = -5x + 30.
Combine the simplified parts of the equation: y = (-2x + 12) + (-5x + 30). Combine like terms: y = -7x + 42.
Set y = 0 to find the values of x: 0 = -7x + 42. Solve for x by isolating x: Subtract 42 from both sides, then divide by -7 to find x.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Solving Equations
Solving equations involves finding the values of the variable that make the equation true. In this case, we need to determine the values of x for which y equals zero. This typically requires isolating the variable on one side of the equation and simplifying the expression.
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Distributive Property
The distributive property states that a(b + c) = ab + ac. This property is essential for simplifying expressions where a term is multiplied by a sum or difference. In the given equation, applying the distributive property will help simplify the expression inside the brackets and the terms outside.
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Combining Like Terms
Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. This step is crucial in solving equations, as it reduces the complexity of the expression, making it easier to isolate the variable and find the solution.
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Related Practice
Textbook Question
In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (4 - i)2 - (1 + 2i)2
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Textbook Question
Solve each absolute value inequality. |3(x - 1)/4| < 6
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Solve each equation in Exercises 65–74 using the quadratic formula.
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Textbook Question
Solve each equation in Exercises 65–74 using the quadratic formula. x2 + 5x + 3 = 0
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Textbook Question
In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 7|5x| + 2 = 16
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