Domanda del libro di testo
Solve each equation in Exercises 41–60 by making an appropriate substitution. x - 13√x + 40 = 0
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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
Capitolo 2, Problema 44
Solve and check: 24 + 3 (x + 2) = 5(x − 12).
Guida verificata passo dopo passo1
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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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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04:15
Multiply Polynomials Using the Distributive Property
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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5:22Combinations
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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05:28Equations with Two Variables
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