Page 445 - Algebra 1

L E S S O N Solving Inequalities by Adding or Subtracting 66
Warm Up
New Concepts
1. Vocabulary A(n)
is a mathematical statement comparing
3. -26 + x = -9 (19)
5. x ≥ -3 (50)
(45)
Solve.
2. x + 13 = 21
(19)
Graph. 4. x < 2
(50)
quantities that are not equal.
Addition Property of Inequality
For any real numbers a, b, and c:
If a<b,thena+c<b+c. If a≤b,thena+c≤b+c. If a>b,thena+c>b+c. If a≥b,thena+c≥b+c.
Example
1
Reading Math
An open circle on the graph of an inequality means that the value is not part of the solution.
Online Connection www.SaxonMathResources.com
Recall that you can add or subtract the same number from both sides of an equation and it remains a true statement. The same is true for inequalities. The Addition Property of Inequality states that when the same number is added to both sides of an inequality, the statement remains true.
Using the Addition Property of Inequality
Solve the inequality x - 10 < -6 and graph the solution on a number line. SOLUTION
x - 10 < -6
+_1_0 +_1_0 Addition Property of Inequality x < 4 Simplify.
The solution includes all values less than, but not including, 4.
02468
The solution to the inequality is x < 4.
Inequalities have an infinite number of solutions. This makes it impossible to check all the solutions. The endpoint and the direction of the inequality can be checked. For example, the solution in Example 1 can be checked using the steps on the following page.
430 Saxon Algebra 1