Page 473 - Algebra 1

Example
4
Dividing by a Negative Number
Solve, graph, and check the solution for the inequality -4m ≥ 7.
SOLUTION
Solve the inequality. -4m ≥ 7
Math Reasoning
Connect Solving inequalities is exactly the same as solving equations. Do you agree or disagree with the statement? Explain.
-4m ≤ 7 __
-4 -4 m ≤ -1_3
Division Property of Inequality for c < 0 Simplify. Write the solution as a mixed number.
4
Graph the solution on a number line.
-3 -2 -1
Check the direction of the inequality. -4m 7
-4(-2) 7 8≥7 ✓
An employment agency charges a company 15% of the salary for every position filled. What salary must a company pay a new employee for the employment agency to earn a commission of at least $6000?
SOLUTION
Check
Check the endpoint. -4m 7
-4(-1_3) 7 4
7=7 ✓
Both statements are true, so the solution is correct.
Application: Business
Example
5
Math Reasoning
Analyze When solving word problems with inequalities, think about what restrictions exist on the solution set. What are restrictions for this business application?
Write and solve an inequality. 0.15s ≥ 6000
__
0.15s ≥ 6000 Division Property of Inequality for c > 0
0.15 0.15
s ≥ 40,000 Simplify.
Any salary of $40,000 or more will earn a commission of at least $6000.
Check
Check the endpoint. Check the direction of the inequality.
0.15s 6000 0.15s 6000 0.15(40,000) 6000 0.15(50,000) 6000
6000 = 6000 ✓ 7500 ≥ 6000 ✓
458 Saxon Algebra 1