(a)
Solve the equation
(a)
Answer to Problem 55HP
Explanation of Solution
Given:
The equation
Concept Used:
Addition or Subtraction Property of Equality:
If
The property that states that if you add or subtract the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)
Multiplication and Division Properties of Equality:
If
If
In other words, if two expressions are equal to each other and you multiply or divide (except for 0) the exact same constant to both sides, the two sides will remain equal.
Calculation:
The equation:
Step1: Use the cross multiplication method:
Solve:
In an equation the variable term in the left side and right side are same, the equation has no solutions (if no value of the variable makes the equation true).
Inconsistent equations: No solutions
For example, 3=3 is an identity equation. An equation like 3=5 is an inconsistent equation, since 3 is not equal to 5. If in the process of solving an equation we end up with an inconsistent equation, then the original equation has no solutions.
Thus, the solution of the equation
(b)
Solve the equation
(b)
Answer to Problem 55HP
Has a solution;
Explanation of Solution
Given:
The equation:
Concept Used:
Addition or Subtraction Property of Equality:
If
The property that states that if you add or subtract the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)
Multiplication and Division Properties of Equality:
If
If
In other words, if two expressions are equal to each other and you multiply or divide (except for 0) the exact same constant to both sides, the two sides will remain equal.
Calculation:
Step1: Use the cross multiplication method:
The equation:
Solve:
Thus, the solution of the equation
(c)
Solve the equation
(c)
Answer to Problem 55HP
Explanation of Solution
Given:
The equation:
Concept Used:
Addition or Subtraction Property of Equality:
If
The property that states that if you add or subtract the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)
Multiplication and Division Properties of Equality:
If
If
In other words, if two expressions are equal to each other and you multiply or divide (except for 0) the exact same constant to both sides, the two sides will remain equal.
Calculation:
The equation:
Solve:
Inconsistent equations: No solutions
For example, 3=3 is an identity equation. An equation like 3=5 is an inconsistent equation, since 3 is not equal to 5. If in the process of solving an equation we end up with an inconsistent equation, then the original equation has no solutions.
Thus, the solution of the equation
Chapter 2 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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