Concept explainers
a.
To solve the equation
a.
Answer to Problem 6CA
Explanation of Solution
Given:
Concept used:
- If an equation is true for all values of the variable, then it is an identity equation.
- If an equation is true for only some values of the variable, then it is a conditional equation.
- If an equation results in a false statement, then it is an inconsistent equation.
Calculation:
Solving the equation,
Now, classifying the equation on the basis of the solution obtained.
Since the solution set consists of one number: {8}, it is the only solution and, therefore, the given equation is conditional.
Conclusion:
Therefore, the solution to the given equation is
b.
To solve the equation
b.
Answer to Problem 6CA
Explanation of Solution
Given:
Concept used:
- If an equation is true for all values of the variable, then it is an identity equation.
- If an equation is true for only some values of the variable, then it is a conditional equation.
- If an equation results in a false statement, then it is an inconsistent equation.
Calculation:
Solving the equation
Now, classifying the equation on the basis of the solution obtained.
Since the solution set consists of one number:
Conclusion:
Therefore, the solution to the given equation is
c.
To solve the equation
c.
Answer to Problem 6CA
Inconsistent equation
Explanation of Solution
Given:
Concept used:
- If an equation is true for all values of the variable, then it is an identity equation.
- If an equation is true for only some values of the variable, then it is a conditional equation.
- If an equation results in a false statement, then it is an inconsistent equation.
Calculation:
Solving the equation
[Subtracting
Since it is a false statement, there is no solution to the given equation and hence, it is an inconsistent equation.
Conclusion:
Therefore, there is no solution to the given equation. It is an inconsistent equation.
d.
To solve the equation
d.
Answer to Problem 6CA
Explanation of Solution
Given:
Concept used:
- If an equation is true for all values of the variable, then it is an identity equation.
- If an equation is true for only some values of the variable, then it is a conditional equation.
- If an equation results in a false statement, then it is an inconsistent equation.
Calculation:
Solving the equation
Now, classifying the equation on the basis of the solution obtained.
Since the solution set consists of one number:
Conclusion:
Therefore, the solution to the given equation is
e.
To solve the equation
e.
Answer to Problem 6CA
Explanation of Solution
Given:
Concept used:
- If an equation is true for all values of the variable, then it is an identity equation.
- If an equation is true for only some values of the variable, then it is a conditional equation.
- If an equation results in a false statement, then it is an inconsistent equation.
Calculation:
Solving the equation
Now, classifying the equation on the basis of the solution obtained.
Since the solution set consists of one number:
Conclusion:
Therefore, the solution to the given equation is
f
To solve the equation
f
Answer to Problem 6CA
Explanation of Solution
Given:
Concept used:
- If an equation is true for all values of the variable, then it is an identity equation.
- If an equation is true for only some values of the variable, then it is a conditional equation.
- If an equation results in a false statement, then it is an inconsistent equation.
Calculation:
Solving the equation
Now, classifying the equation on the basis of the solution obtained.
Since the solution set consists of all values that make the statement true. For this equation, the solution set is all real numbers because any real number substituted for
Conclusion:
Therefore, the solution set to the given equation is all real numbers and it is an identical equation.
Chapter 3 Solutions
BIG IDEAS MATH Algebra 1: Common Core Student Edition 2015
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