review 2.1-2.5 advanced algebra 1. word problems with inequalities don’t panic! remember to: read...
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Review 2.1-2.5Advanced Algebra 1
Word Problems with Inequalities
Don’t panic! Remember to: •Read the questions carefully.•Define the variable.•Write an inequality.•Solve the inequality.•Check that your answer is reasonable.•Answer in a complete sentence.
Example 1Eight less than the product of -3 and a number is greater than -26. Write and solve an inequality to represent this relationship. Graph the solution set, and check your answer.
Let x = the number-3x – 8 > -26
+8 +8 -3x > -18 -3 -3 x < 6
4 5 6 7 8
CHECK @ x = 5-2x – 6 > -18 -2(5) – 6 > -18-10 – 6 > -18-16 > -18 Don’t forget to reverse the inequality
sign when dividing by a negative!
Example 2 The sum of two consecutive integers is at least negative fifteen. What are the smallest values of consecutive integers that will make this true?
Let x = the first integer x + 1 = the next consecutive integer
x + (x + 1) ≥ -15 2x + 1 ≥ -15
- 1 - 1 2x ≥ -16
2 2 x ≥ -8
x + 1 ≥ -7
The smallest values of consecutive integers
that will add to at least -15 are -8 and -7.
Example 3Connor went to the carnival with $22.50. He bought a hot dog and a drink for $3.75, and he wanted to spend the rest of his money on ride tickets which cost $1.25 each. What is the maximum number of ride tickets that he can buy?
Let r = the number of ride tickets he can buy
cost of food + cost of rides ≤ $22.50
3.75 + 1.25r ≤ 22.50 -3.75 -3.75 1.25r ≤ 18.75 1.25 1.25 r ≤ 15 tickets
Connor can buy a maximum of 15 ride tickets.
Example 4Stan earned $7.55 per hour plus an additional $100 in tips waiting tables on Saturday evening. He earned $160 in all. To the nearest hour, what is the least number of hours Stan would have to work to earn this much money?
Let h = the number of hours Stan will have to work
tips + hourly wages ≥ $160
100 + 7.55h ≥ 160 -100 -100 7.55h ≥ 60 7.55 7.55 x ≥ 7.9 hours
To the nearest hour, Stan would have to work at least 8 hours to earn $160.
Example 5Brenda has $500 in her bank account. Every week, she withdraws $40 for expenses. Without making any deposits, how many weeks can she withdraw this money if she wants to maintain a balance of at least $200?
Let w = the number of weeks Brenda withdraws money
starting account balance – money withdrawn ≥ $200
500 – 40w ≥ 200 -500 -500 – 40w ≥ -300
– 40 – 40 w ≤ 7.5 weeks
Don’t forget to reverse the inequality sign when dividing by a negative!
Brenda can withdraw $40 from the account for 7 full weeks and still have at least $200 in the account.
Example 3
x < 2x – 15
3
3x < 2x – 15
-2x -2x
x < -15
(3)(3)
TOO
1. -3 > -3t + 6
2. 26p – 20 > 14p + 64
3. .
1. t > 3
2. p > 7
3. t < -19
38
2
t
Special Case #1
3x + 4 > 2(x + 3) + x
3x + 4 > 2x + 6 + x
3x + 4 > 3x + 6
-3x -3x
4 > 6
• Distribute
•Combine like terms
•Get variable on same side
•True or false?
This state is FALSE:
No Solution
Special Case #2
3 – 3(y – 2) < 13 – 3(y – 6)
3 – 3y + 6 < 13 – 3y + 18
-3y + 9 < -3y + 31
+3y + 3y
9 < 31
• Distribute
•Combine like terms
•Get variable on same side
•True or false?
This state is TRUE:
All Numbers
Solve each inequality.
3 3 6t 3t
23 7
3w 15w
8 2 10 20n n 9n
Solve each inequality.
5 4 8 2 17m m 15m
2 15
3
xx
15x
6 2 4 12p p 7p
Solve each inequality.
3( 2) 8 44x x 10x
5( 4) 3( 4)k k 1k
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