1. Algebra 2 Lesson 1-4 (Page 26)
Solving Inequalities
ALGEBRA 2 LESSON 1-4
Algebra 2
Lesson 1-4
(Page 26)
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2. Properties of Inequalities (Page 26)
Solving Inequalities
ALGEBRA 2 LESSON 1-4
Properties of Inequalities (Page 26)
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3. To solve and graph inequalities.
Solving Inequalities
ALGEBRA 2 LESSON 1-4 7
To solve and graph inequalities.
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4. Solving and Graphing Inequalities
Solving Inequalities
ALGEBRA 2 LESSON 1-4
Solving and Graphing Inequalities 7
Solve –2x < 3(x – 5). Graph the solution.
–2x < 3(x – 5)
–2x < 3x – 15 Distributive Property
–5x < –15 Subtract 3x from both sides.
x > 3 Divide each side by –5 and reverse the inequality.
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5. Solving and Graphing Inequalities
Solving Inequalities
ALGEBRA 2 LESSON 1-4
Solving and Graphing Inequalities 7
Solve the inequality. Graph the solution.
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6. Solving and Graphing Inequalities
Solving Inequalities
ALGEBRA 2 LESSON 1-4
Solving and Graphing Inequalities 7
Solve the inequality. Graph the solution.
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7. No Solutions or All Real Numbers as Solutions
Solving Inequalities
ALGEBRA 2 LESSON 1-4
No Solutions or All Real Numbers as Solutions 7
Solve 7x 7(2 + x). Graph the solution.
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7x 7(2 + x)
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7x x Distributive Property
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Subtract 7x from both sides.
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The last inequality is always false, so 7x 7(2 + x) is always false.
It has no solution.
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8. No Solutions or All Real Numbers as Solutions
Solving Inequalities
ALGEBRA 2 LESSON 1-4
No Solutions or All Real Numbers as Solutions 7
Solve the inequality. Graph the solution.
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9. No Solutions or All Real Numbers as Solutions
Solving Inequalities
ALGEBRA 2 LESSON 1-4
No Solutions or All Real Numbers as Solutions 7
Solve the inequality. Graph the solution.
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10. HOT 7 Solving Inequalities
ALGEBRA 2 LESSON 1-4
HOT 7
A real estate agent earns a salary of $2000 per month plus 4% of the sales. What must the sales be if the salesperson is to have a monthly income of at least $5000?
Relate: $ % of sales $5000
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Define: Let x = sales (in dollars).
Write: x
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0.04x Subtract 2000 from each side.
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x 75,000 Divide each side by 0.04.
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The sales must be greater than or equal to $75,000.
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11. HOT 7 Solving Inequalities
ALGEBRA 2 LESSON 1-4
HOT 7
A salesperson earns a salary of $700 per month plus 2%
of the sales. What must the sales be if the salesperson is to have a
Monthly income of at least $1800?
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12. To solve and write compound inequalities.
Solving Inequalities
ALGEBRA 2 LESSON 1-4 8
To solve and write compound inequalities.
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13. A compound inequality is a pair of Inequalities joined by and or or.
Solving Inequalities
ALGEBRA 2 LESSON 1-4
New Vocabulary
A compound inequality is a pair of
Inequalities joined by and or or.
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14. Solving Inequalities
ALGEBRA 2 LESSON 1-4 8
Graph the solution of 2x – x and x > 4x – 9.
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2x – x and x > 4x – 9
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–1 x > 3x
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– x and 3 > x
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This compound inequality can be written as –1 x < 3.
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15. Solving Inequalities
ALGEBRA 2 LESSON 1-4 8
Graph the solution of 2x – x and x > 4x – 9.
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16. Solving Inequalities
ALGEBRA 2 LESSON 1-4 8
Graph the solution of
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17. Solving Inequalities
ALGEBRA 2 LESSON 1-4 8
Graph the solution of 3x + 9 < –3 or –2x + 1 < 5.
3x + 9 < –3 or –2x + 1 < 5
3x < – –2x < 4
x < –4 or x > –2
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18. Solving Inequalities
ALGEBRA 2 LESSON 1-4 8
Graph the solution of 3x + 9 < –3 or –2x + 1 < 5.
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19. Solving Inequalities
ALGEBRA 2 LESSON 1-4 8
Solve the compound inequality and graph the solution.
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20. Solving Inequalities
ALGEBRA 2 LESSON 1-4 8
Solve the compound inequality and graph the solution.
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21. HOT 8 Solving Inequalities
ALGEBRA 2 LESSON 1-4
HOT 8
A strip of wood is to be 17 cm long with a tolerance of ± 0.15 cm. How much should be trimmed from a strip 18 cm long to allow it to meet specifications?
Relate: minimum length final length maximum length
Define:  Let x = number of centimeters to remove.
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Write: 17 – – x
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– x Simplify.
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– – x –0.85 Subtract 18.
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x Multiply by –1.
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At least 0.85 cm and no more than 1.15 cm should be trimmed off to meet specifications.
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22. HOT 8 Solving Inequalities
ALGEBRA 2 LESSON 1-4
HOT 8
The plans for a circular plastic part in an insulin pump require
A diameter of 1.5in. with a tolerance of +0.2in. A machinist finds that the
diameter is now 1.73in. By how much should the machinist decrease the
diameter.
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