Page 497 - Algebra 1

Any number that satisfies both inequalities is a solution of a conjunction. A conjunction can be solved as two inequalities connected with AND or as an inequality with three parts, such as 8 ≥ x ≥ 3.
Solving Conjunctions
A cellular phone contract includes a monthly usage fee of $10 plus an additional $0.10 per minute of talk time. Suppose that the monthly cell phone bill is between $30 and $40. Write a compound inequality that describes the situation. Solve the inequality to find the number of minutes that can be used to keep the monthly bill within the desired amounts.
SOLUTION
Write and solve the conjunction as two separate inequalities connected with AND.
Reading Math
< means is less than.
> means is greater than and is more than.
≤ means is less than or equal to, is at most, is no more than.
≥ means is greater than or equal to, is at least, is no less than.
≤ and ≥ are used with the word inclusive while < and > are used with the word between.
Example
2
Method 1:
30 ≤10+0.10x
be used monthly.
Method 2:
Write and solve the conjunction as 30 ≤ 10 + 0.10x ≤ 40. 30 ≤ 10 + 0.10x ≤ 40
20 ≤ 0.10x ≤ 30 Subtract 10 from each part of the inequality. 200 ≤ x ≤ 300 Divide each part of the inequality by 0.10.
The solution is 200 ≤ x ≤ 300. Between 200 and 300 minutes, inclusive, can be used monthly.
A disjunction is a compound inequality that uses the word OR. Disjunctions must be written as two separate inequalities connected with the word OR. A solution to these inequalities is any number that makes either inequality true.
Writing and Graphing Disjunctions
Write and graph a compound inequality to represent the statement.
a. all real numbers greater than 9 or less than 3 SOLUTION
AND 10+0.10x≤40 | 0.10x ≤ 30
AND x ≤ 300
The solution is 200 ≤ x ≤ 300. Between 200 and 300 minutes, inclusive, can
Math Reasoning
Justify Why is there
no solution for the conjunction x < -2 AND x > 3?
20 ≤0.10x 200 ≤ x
Example
3
x < 3 OR x > 9
0 2 4 6 8 10
b. all real numbers no more than 7 and no less than 11 SOLUTION
x ≤ 7 OR x ≥ 11
4 6 8 10 12 14
482 Saxon Algebra 1