Domanda del libro di testo
Solve each radical equation in Exercises 11–30. Check all proposed solutions.
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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 19
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2(x-4)+3(x+5)=2x-2
Guida verificata passo dopo passo1
Start by applying the distributive property to both sides of the equation: expand \(2(x-4)\) and \(3(x+5)\) to get \(2 \cdot x - 2 \cdot 4 + 3 \cdot x + 3 \cdot 5\).
Simplify the expressions on the left side by performing the multiplications: this results in \(2x - 8 + 3x + 15\).
Combine like terms on the left side: add \$2x$ and \$3x$ to get \$5x$, and combine $-8$ and \(15\) to get \(7\), so the left side becomes \(5x + 7\).
Rewrite the equation with the simplified left side and the right side as is: \(5x + 7 = 2x - 2\).
To isolate \(x\), subtract \$2x$ from both sides and subtract \(7\) from both sides, resulting in \(5x - 2x = -2 - 7\), which simplifies to \(3x = -9\). From here, you can solve for $x$ by dividing both sides by 3.
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Solving Linear Equations
Solving linear equations involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, and division. The goal is to find the value of the variable that makes the equation true. For example, simplifying and combining like terms helps to reduce the equation to a simpler form.
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Solving Linear Equations with Fractions
Types of Equations: Identity, Conditional, and Inconsistent
An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solution. After solving, if the equation simplifies to a true statement like 0=0, it is an identity; if it results in a false statement like 0=5, it is inconsistent.
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Distributive Property
The distributive property allows you to multiply a single term by each term inside parentheses, expressed as a(b + c) = ab + ac. This property is essential for expanding expressions before combining like terms and simplifying equations, as seen in 2(x-4) + 3(x+5).
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04:15Multiply Polynomials Using the Distributive Property
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