Page 329 - Algebra 1

L E S S O N Graphing Inequalities 50
Warm Up
1. Vocabulary A(n) __________ is a mathematical statement that compares
(45)
quantities that are not equal.
2. Translate the sentence below into an inequality.
(45)
Simplify.
3. 8y - 3 = 15 4. 7 = 5x + 4
(23) (23)
137 is at least 13 less than twice a number.
New Concepts A linear inequality in one variable is an inequality that can be written as
ax < b, ax > b, ax ≤ b, ax ≥ b, or ax ≠ b, where a and b are real numbers.
Unlike equations, inequalities can have more than one numeric solution.
The solution of an inequality in one variable is a value or set of values that satisfies the inequality. To determine if a value is a solution to an inequality, substitute the value of the variable into the equation and simplify. If the inequality statement is true, the value is part of the solution set.
Identifying Solutions to Inequalities
Determine which of the values {0, 2, 4, 6} are part of the solution set of the inequality 4y - 5 ≥ 11.
SOLUTION
Substitute each value into the inequality. y=0 y=2
4 · 0 - 5 ≥ 11 4 · 2 - 5 ≥ 11
Math Language
The expression ax ≠ 0 means that x can equal any number except zero.
Example
1
0 - 5 ≥ 11
- 5 ≥ 11; false
8 - 5 ≥ 11
3 ≥ 11; false
Online Connection www.SaxonMathResources.com
y=4 y=6
4 · 4 - 5 ≥ 11 4 · 6 - 5 ≥ 11
16 - 5 ≥ 11 24 - 5 ≥ 11
11 ≥ 11; true 19 ≥ 11; true
The solution set for 4y - 5 ≥ 11 includes 4 and 6.
314 Saxon Algebra 1