Solution Set

Definition

The solution set of an equation is the set of all values of the variable(s) that make the equation true. It represents the complete set of solutions that satisfy the given equation.

5 Must Know Facts For Your Next Test

1. The solution set of an equation is the set of all values of the variable(s) that make the equation true.
2. When solving equations with decimals, the solution set represents the value(s) of the variable that satisfy the equation.
3. The addition and subtraction properties of equality are used to isolate the variable and find the solution set of an equation.
4. Equations with variables and constants on both sides require the use of the addition and subtraction properties of equality to find the solution set.
5. The solution set is an important concept in algebra as it allows you to determine the value(s) of the variable(s) that make an equation true.

Review Questions

• Explain how the solution set of an equation is determined when solving equations with decimals.
  • When solving equations with decimals, the solution set represents the value(s) of the variable that satisfy the equation. This is achieved by using the properties of equality, such as adding or subtracting the same value from both sides of the equation, to isolate the variable and find the value(s) that make the equation true. The solution set is the set of all these values that solve the equation.
• Describe the role of the addition and subtraction properties of equality in finding the solution set of an equation.
  • The addition and subtraction properties of equality are crucial in solving equations and determining the solution set. These properties allow you to isolate the variable by performing the same operation (addition or subtraction) on both sides of the equation. This helps you find the value(s) of the variable that make the equation true, which constitute the solution set. The solution set represents the complete set of values that satisfy the given equation.
• Analyze how the solution set of an equation is affected when the equation has variables and constants on both sides.
  • When an equation has variables and constants on both sides, the solution set is determined by using the addition and subtraction properties of equality to isolate the variable. This involves performing the same operations on both sides of the equation to eliminate the constants and isolate the variable. The value(s) of the variable that make the equation true constitute the solution set, which represents the complete set of solutions that satisfy the given equation with variables and constants on both sides.

Related terms

Equation:

A mathematical statement that expresses the equality of two expressions, often involving variables.

Variable:

A symbol, usually a letter, that represents an unknown or changeable value in an equation.

Equality:

The state or relation of being equal; equivalence in value, measure, force, meaning, or the like.