Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 76a

Capitolo 2, Problema 76a

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7

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Start by isolating the variable term on one side of the equation. Subtract 2x from both sides of the equation:

5x + 7 - 2x = 2x + 7 - 2x

Simplify the equation by combining like terms:

(5x - 2x) + 7 = 7

, which simplifies to

3x + 7 = 7

Next, isolate the term with the variable by subtracting 7 from both sides:

3x + 7 - 7 = 7 - 7

Simplify the equation further:

3x = 0

Finally, solve for

x

by dividing both sides of the equation by 3:

x = \(\frac{0}{3}\)

. After solving, determine whether the equation is an identity, a conditional equation, or an inconsistent equation based on the solution.

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Types of Equations

In algebra, equations can be classified into three main types: identities, conditional equations, and inconsistent equations. An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solutions. Understanding these classifications helps in determining the nature of the solution set for any given equation.

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Types of Slope

Solving Linear Equations

Solving linear equations involves isolating the variable to find its value. This typically includes combining like terms, using inverse operations, and simplifying both sides of the equation. For the equation 5x + 7 = 2x + 7, one would rearrange the terms to isolate x, which is essential for determining the type of equation it represents.

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Solving Linear Equations with Fractions

Checking Solutions

After solving an equation, it is crucial to check the solution by substituting it back into the original equation. This verification process confirms whether the solution is valid and helps identify the type of equation. For instance, if the left-hand side equals the right-hand side after substitution, it indicates whether the equation is an identity or a conditional equation.

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Restrictions on Rational Equations

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