Warm Up: Linear Inequalities in One Variable
Completion requirements
Warm Up |
Linear Inequalities in One Variable
An inequality is a mathematical statement that compares two quantities using the symbols \(\lt\), \(\gt\), \(\le\), or \(\ge\). An inequality is said to be strict if the two sides of the inequality are never equal.
| Inequality | Meaning
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\(a \lt b\)
|
\(a\) is less than \(b\) |
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\(a \gt b\)
|
\(a\) is greater than \(b\) |
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\(a \le b\)
|
\(a\) is less than or equal to \(b\) |
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\(a \ge b\)
|
\(a\) is greater than or equal to \(b\) |
Inequalities in one variable can be represented on a number line using an arrow. The arrow represents all the values that are part of the solution set. If the inequality is strict, an open circle is used to show the endpoint is not included. If the inequality is not strict, a closed circle is used to show the endpoint is included.
\(r \lt 2\)
\(x \ge -7\)
More complex linear inequalities can be solved to determine the values that make the inequality true. Solving a linear inequality in one variable is similar to solving a linear equation in one variable with the following exceptions:
- When multiplying both sides of an inequality by a negative value, reverse the direction of the inequality sign.
-
When dividing both sides of an inequality by a negative value, reverse the direction of the inequality sign.
If \(r \gt s\), then \(-r \lt -s\). This statement is the basis of these two rules. Think about why the statement is true and how the two rules follow from it.