Solve the Inequality
-12 > x - 7
-12 > x - 7
-12 + 7 > x
-5 > x
Graph the solved inequality:
-1 + r ≥ 4
-1 + r ≥ 4
r ≥ 5
solid dot on 5 and shaded to the right (6,7,8, etc)
Write the inequality:
Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2. How many books can he afford without spending more than his gift voucher amount?
$4 * book + $2 = amount Brett spends on books
He wants to spend no more than his voucher, so he wants to spend less than or equal to that amount.
4b + 2 ≤ 30
-3x > 3
-3x > 3
-3x/-3 > 3/-3
x < -1
Graph the solved inequality:
k /4 < -4
k /4 < -4
k < -16
open dot on -16 and shaded to the left (-17,-18,-19...)
Write the inequality:
Lucas is offered either 15% off or $21 off his total shopping bill. How much would have to be spent to make the 15% option the best one?
15% = .15
We want 15% off the bill to make the bill less than if you took $21 off.
.15 * bill < b - 21
2x + 4 ≥ 24
2x + 4 ≥ 24
2x ≥ 24- 4
2x ≥ 20
x ≥ 20/2
x ≥ 10
Graph the solved inequality:
-4b - 5 > -25
-4b - 5 > -25
-4b > -20
b < 5
open circle on 5 and shaded to the left
Solve the word problem.
Sid is $300 in debt. He needs to get the debt down to no more than $100 within the next 8 months. If he pays the same amount each month, what is the minimum he must pay off each month to manage this?
300 = current debt
8 * amount he pays per month will be taken out of that debt
He needs the debt to be less than or equal to $100.
300 - 8m ≤ 100
-8m ≤ 100 - 300
-8m ≤ -200
m ≥ -200/-8
m ≥ 25
The minimum he could pay each month is $25.
-90 ≥ -5 (k - 3)
-90 ≥ -5 (k - 3)
-90/-5 ≤ k- 3
18 ≤ k - 3
18 + 3 ≤ k
21 ≤ k
Graph the solved inequality:
(-8 + r) / 2 > -8
(-8 + r) / 2 > -8
-8 + r > -16
r > -8
open circle on -8 and shaded to the right (-7,-6,-5...)
Solve the word problem:
The sum of two consecutive integers is at least negative fifteen. What are the smallest values of consecutive integers that will make this true?
Consecutive numbers are numbers in a row (ex: 3,4,5). If the first number is x, the next number is x + 1.
x + (x + 1) ≥ -15
2x + 1 ≥ -15
2x ≥ -15 -1
2x ≥ -16
x ≥ -16/2
x ≥ -8
The smallest value of the integers are -8 and -7 (-8 +1)
-3 - 6(4x + 6) > -111
-3 - 6(4x + 6) > -111
-6(4x + 6) > -111 + 3
-6(4x + 6) > -108
(4x + 6) < -108/-6
4x + 6 < 18
4x < 18 - 6
4x <12
x < 12/4
x < 3
Graph the solved inequality:
-5n + 6 ≥ -7(5n - 6) - 6n
-5n + 6 ≥ -7(5n - 6) - 6n
-5n + 6 + 6n ≥ -7(5n - 6)
6 + n ≥ -7(5n - 6)
6 + n ≥ -35n + 42
6 + n + 35n ≥ 42
6 + 36n ≥ 42
36n ≥ 42 - 6
36n ≥ 36
n ≥ 36/36
n ≥ 1
solid circle on 1 and shaded to the right (2,3,4...)
Solve the word problem:
Commission or salary: Jill has a job offer. She is offered either $50 per day or $30 per day plus a commission of $3 for every plant she sells. How many plants does she need to sell to make the commission offer the best paying option, assuming she works the same number of days?
$50d < $30d + $3p
$50d - $30d < $3p
$20d < $3p
$20d/ $3 < p
20/3 d < p
6.67 d < p
The number of plants must be 7x greater (you cannot sell a fraction of a plant) than the number of days she words OR the commission makes sense if she is selling at least 7 plants a day.