Solution Set

Definition

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

5 Must Know Facts For Your Next Test

1. The solution set of an equation or inequality can be a single value, a set of values, or even an infinite set of values.
2. The solution set of an equation with variables on both sides can be found by isolating the variable and solving for it.
3. The solution set of a linear inequality can be represented on a number line or a coordinate plane.
4. The solution set of a system of equations can be found by using substitution, elimination, or graphing methods.
5. The solution set of a system of linear inequalities can be represented as the intersection of the individual solution sets.

Review Questions

• Explain how to find the solution set of an equation with variables and constants on both sides.
  • To find the solution set of an equation with variables and constants on both sides, you need to isolate the variable by performing the same operations on both sides of the equation. This may involve adding, subtracting, multiplying, or dividing to get the variable by itself on one side. Once the variable is isolated, you can solve for its value, which represents the solution set of the equation.
• Describe how the solution set of a linear inequality is represented on a number line or coordinate plane.
  • The solution set of a linear inequality can be represented on a number line or a coordinate plane. On a number line, the solution set is the set of all points that satisfy the inequality, which may be an interval or a union of intervals. On a coordinate plane, the solution set is the region that satisfies the inequality, which is typically a half-plane or the intersection of half-planes.
• Analyze how the solution set of a system of linear inequalities is determined by the intersection of the individual solution sets.
  • The solution set of a system of linear inequalities is the set of all points that satisfy all the inequalities in the system. To find this solution set, you need to graph each individual inequality on a coordinate plane and then identify the region where all the individual solution sets overlap. This intersection represents the solution set of the entire system of linear inequalities, which may be a polygon, a half-plane, or even the empty set if the inequalities are inconsistent.

Related terms

Equation:

A mathematical statement that two expressions are equal, often containing one or more variables.

Inequality: A mathematical statement that compares two expressions using symbols such as >, <, ≥, or ≤.

Variable:

A symbol, usually a letter, that represents an unknown or changeable quantity in a mathematical expression.