Essential Understanding Sometimes, no value of the variable makes an equation true. For identities, all values of the variable make the equation true.
Problem 4 Equations With No Solution and Identities
Is the equation always, sometimes, or never true?
Think
What does it mean for an equation to be sometimes true?
An equation is sometimes true if it is true for some, but not all, values of the variable.
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The last equation is not true, so no value of x makes the first two equations true. The original equation has no solution. It is never true.
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The last equation is true, so any value of x makes the first three equations true. The original equation is always true. It is an identity.
✓ Got It?
- Is the equation always, sometimes, or never true?
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A literal equation is an equation that uses at least two different letters as variables. You can solve a literal equation for any one of its variables by using the properties of equality. You solve for a variable “in terms of” the other variables.
Problem 5 Solving a Literal Equation
The equation
Plan
How do you solve a literal equation for one of its variables?
Use inverse operations to isolate the indicated variable.
✓ Got It?
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- The equation K = C + 273 relates temperatures kelvins K and degrees Celsius C. What is C in terms of K?
- Reasoning Is the equation relating temperatures in kelvins and degrees Celsius always, sometimes, or never true? Explain your answer.
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions