Transcript PPT Review 2.1

Review 2.1-2.5
Advanced 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 1
Eight 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
Don’t forget to reverse the inequality
sign when dividing by a negative!
4
5
6
7
8
CHECK @ x = 5
-2x – 6 > -18
-2(5) – 6 > -18
-10 – 6 > -18
-16 > -18
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 3
Connor 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 4
Stan 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 5
Brenda 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starting account balance – money withdrawn ≥ $200
Don’t forget
to reverse the
inequality sign
when dividing
by a negative!
500 – 40w ≥ 200
-500
-500
– 40w ≥ -300
– 40
– 40
w ≤ 7.5 weeks
Brenda can withdraw $40
from the account for 7 full
weeks and still have at
least $200 in the account.
Example 3
(3) x < 2x – 15 (3)
3
3x < 2x – 15
-2x -2x
x < -15
TOO
1. -3 > -3t + 6
2. 26p – 20 > 14p + 64
1. t > 3
2. p > 7
3. . t  3  8
2
3. t < -19
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) • Distribute
3 – 3y + 6 < 13 – 3y + 18 •Combine like terms
•Get variable on
-3y + 9 < -3y + 31
same side
+3y
+ 3y
•True or false?
9 < 31
This state is TRUE:
All Numbers
Solve each inequality.
3  3t  6
t 3
2
w3 7
3
w  15
8n  2 10n  20
n  9
Solve each inequality.
5  4m  8  2m  17
2 x  15
x
3
m  15
x  15
6 p  2  4 p  12
p7
Solve each inequality.
3( x  2)  8 x  44
x  10
5(k  4)  3(k  4)
k  1