Read & Write: Inequality
#6
GMS hopes to raise more than $3000 for the Pickens County Animal Shelter. Every time a student donates $40 they would get to pie a math teacher in the face. How many donations would it take for GMS to reach or exceed its goal?
40x ≥ 3000
#1
Aliyah had $24 to spend on seven pencils. After buying them, she had $10. How much did each pencil cost?
24 - 7x = 10
or
-7x + 24 = 10
#25
9 > 24 - 5n
3 < n
or
n > 3
#9
6a + 5a = -11
a = -1
#3
The seventh grade class is putting on a variety show to raise money. Renting the banquet hall costs $100. If they charge $10 for each ticket, how many tickets do they need to sell in order to raise at least $100?
10x - 100 ≥ 100
#2
Johnny won 40 super gigantic Blow Pops playing BINGO at his school’s game night. Later, he gave 2 to each of his friends. He only has 8 remaining. How many friends did she give super gigantic Blow Pops to?
2x + 8 = 40
#27
m/3 - 3 ≥ -6
m ≥ -9
#10
6r - 1 + 3r = 26
r = 3
#5
Christina goes to the market with $50. She buys a papaya for $20 and spends the rest of the money on bananas. Each banana costs $6. What is the most bananas Christina can purchase?
6x + 20 ≤ 50
#7
DJ wanted to buy a snack at the school dance. He has $25 to spend on the ticket and snacks. The ticket costs $5 and each snack costs $1.25. How many snacks could DJ buy?
1.25x + 5 = 25
#15
8(1 + 2x) < 32
x < 1.5
or
x < 32/24
#18
-(2n - 8)= -2
n = 5
#20 Here's is Dave's Problem
(2x + 1) / 3 > 5
Dave thinks the first way to solve this problem is to divided by 3. This is what he rewrote.
2/3x + 1/3 > 5/3
Is this correct?
If no, then what should he have done, and how should he have rewrote this step?
First, you MULTIPLY by 3 and rewrite the problem as:
2x + 1 > 15
#4
Daniel had $50 to spend at the South Carolina State Fair. Admission to the fair is $15, and the rides cost $2.50 each. What is the greatest number of rides Daniel can go on?
2.50x + 15 ≥ 50
#8
Elly is saving to purchase a digital camera for $490. Currently, Elly has $287 in her bank account. If she earns $9.50 per hour babysitting, how many hours does she need to babysit before she has enough money to buy the camera?
9.50x + 287 = 490
#28
1/2(-4x + 5) + 1.5 > 16
x < -6
#29
-7(x + 1) = -56
x = 7
#21 Here is Dave's Problem
3(3x - 6) ≤ 18
First, he multiplied by 3 across the parenthesis and got:
9x - 18 ≤ 18
Second, using his V/C chart, he combined +18 and
-18 and got:
9x ≤ 0
Which Step did he do correctly. Which Step did he do incorrectly. Lastly, make the correction to Dave's work.
1st Step was correct
2nd Step was INCORRECT
On step 2 he should have combined +18 and +18 in his V/C chart and got:
9x ≤ 36
#24 Here's Dave's Problem
-2 ≥ 4p + 10
Using his V/C chart, Dave combined -2 and -10 and got:
-12 ≥ 4p
Then, he divided by 4 on each side of the inequality and got:
3 ≥ p
Which Step did he do correctly. Which Step did he do incorrectly. Lastly, make the correction to Dave's work.
1st Step was correct
2nd Step was INCORRECT
On step 2, dividing by 4 on each side should have gotten him:
-3 ≥ p or p ≤ -3