Question

q3 - accelerated mathematics gr 8 | guided notes: solving and graphing linear inequalities in one-variable

1. an inequality that includes variables and ______ represents a relationship where one variable does not strictly equal another.
2. a(n) ______ inequality allows for the inclusion of the boundary value in the solution set.
3. when adding or subtracting the same number from both sides of an inequality, the relationship between the sides remains ______.
4. inequalities that use the symbols ≠ represent ______ relationships.
5. the ______ of an inequality graphically shows where the variables values lie in relation to the inequality condition.

Explanation:

1. The first blank defines a linear inequality (with variables and an inequality symbol) as a non-strict equality relationship.
2. "Inclusive" inequalities use ≤ or ≥, which include the boundary value.
3. The addition/subtraction property of inequalities states the relationship stays unchanged when adding/subtracting the same number to both sides.
4. The symbols ≠ represent non-equivalent, or not equal, relationships.
5. A graph of an inequality uses a number line to show the solution set, which is the visual representation of valid variable values.

Answer:

1. An inequality that includes variables and an inequality symbol represents a relationship where one variable does not strictly equal another.
2. A(n) inclusive inequality allows for the inclusion of the boundary value in the solution set.
3. When adding or subtracting the same number from both sides of an inequality, the relationship between the sides remains unchanged.
4. Inequalities that use the symbols ≠ represent not equal / non-equivalent relationships.
5. The graph / solution set graph of an inequality graphically shows where the variable's values lie in relation to the inequality condition.