Textbook Question
Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.
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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 44
Solve and check: 24 + 3 (x + 2) = 5(x − 12).
Verified step by step guidance1
Distribute the 3 on the left side: 24 + 3(x + 2) becomes 24 + 3x + 6.
Combine like terms on the left side: 24 + 6 becomes 30, so the equation is 3x + 30.
Distribute the 5 on the right side: 5(x - 12) becomes 5x - 60.
Set the equation: 3x + 30 = 5x - 60.
Rearrange the equation to isolate x: Subtract 3x from both sides to get 30 = 2x - 60, then add 60 to both sides to solve for x.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Distributive Property
The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term inside a parenthesis. In the given equation, applying the distributive property is essential to simplify expressions like 3(x + 2) and 5(x - 12) before solving for x.
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Combining Like Terms
Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This step is crucial in simplifying equations to isolate the variable. In the equation provided, after applying the distributive property, combining like terms will help in simplifying both sides of the equation to solve for x.
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Isolating the Variable
Isolating the variable means rearranging the equation to get the variable (in this case, x) on one side and the constants on the other. This process often involves using inverse operations, such as addition, subtraction, multiplication, or division. Successfully isolating x will lead to the solution of the equation.
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Related Practice
Textbook Question
In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 3 - √-7)2
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Textbook Question
Use the graph to a. determine the x-intercepts, if any; b. determine the y-intercepts, if any. For each graph, tick marks along the axes represent one unit each.
Textbook Question
Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 7/2x - 5/3x = 22/3
Textbook Question
In Exercises 45–47, solve each formula for the specified variable. vt + gt^2 = s for g
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Textbook Question
In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.