Page 447 - Algebra 1

Just as you can add the same number to both sides of an inequality, you can also subtract the same number from each side. When equal quantities are subtracted from both sides of an inequality, the inequality remains true.
Using Subtraction
Solve the inequality x + 2 > 3. Then graph and check the solution. SOLUTION
x+2>3
-__2 -__2 Subtraction Property of Inequality x > 1 Simplify.
Subtraction 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
3
The solution is x > 1.
Check
-2 0 2 4 6
Check the endpoint. Check the direction of the inequality.
x+2=3 x+2>3 1+2 3 2+2 3
3=3 ✓ 4>3 ✓ Thesolutionof x+2>3isx>1.
Application: Travel
An airline allows a suitcase that weighs no more than 50 pounds when it is full. Jared’s empty suitcase weighs 5 pounds. How much weight can Jared pack in his suitcase? Write an inequality to solve the problem. Check your solution.
SOLUTION
Write an inequality to represent the situation. Then solve the inequality. x + 5 ≤ 50
Example
4
x ≤ 45 Subtract 5 from both sides. Jared can pack no more than 45 pounds. Check
Check the endpoint.
Hint
To check an inequality solution, try substituting in numbers that are part of the solution set.
432 Saxon Algebra 1
x + 5 = 50 45 + 5 50
x + 5 ≤ 50 44 + 5 50
50=50 ✓
49≤50 ✓
Check the direction of the inequality.