Solve
3x+5=-16
x= -7
Inverse of subtraction
Addition
What error was made on #13 in the review packet?
She should have subtracted both sides by 6 first, not divide by 3
An Uber charges $5 upfront and $2 per mile. A different ride service charges $10 upfront and $1.50 per mile. After how many miles will the cost of both services be the same?
5+2m=10+1.50m
What the the steps to solving an equation?
(Q8)
Draw the line, Distribute, Combine like terms, Add/Subtract, Multiply/Divide
−2m − 9 = 6m + 15
m= -3
Inverse of multiplication. (Q18)
division
-4(5x - 1) + 16x = 40
-20 x + 4 +16 x = 40
-36 x + 4 = 40
- 4 - 4
-36 x = 36
Divide -36 -36
x = -1
(Q14)
On the third line he thought that -20x and +16x was equal to -36x and it should be equal to -4x
Carlos and Mia collect baseball stickers. Carlos has 80 baseball cards and collects 12 cards per week. Mia has 140 baseball cards and collects 6 cards per week. After how many weeks will Carlos and Mia have the same number of baseball cards?
(Q7)
80+12w=140+6w
What mathematical operation are you doing when you distribute?
Multiplication
–5n + 3 = n – 21
(Q15)
n=4
Inverse of division
multiplication
-2(2w-9) = -38
-4w-18 = -38
+18 = +18
-2 times -9 would be positive 18 not negative 18
A group of 6 students went bowling. Each student rented bowling shoes for $x and spent $8 on snacks. A group of 4 adults also went bowling and paid twice as much to rent bowling shoes as each student. Each adult also spent $9.50 on snacks. If both groups spent the same total amount, what was the cost for each adult to rent bowling shoes?
6(x+8)=4(2x+9.50)
Combine like terms
4x-2+7x-8-3x
(Q17)
8x-10
3 ( 4x + 6 ) = 2 ( 5x + 4 )
x=-5
The inverse of a square root
Squaring
−8n + 4(1+5n) = −6n −14
−8n + 4+5n = −6n −14
−3n + 4 = −6n −14
+6n +6n
3n + 4 = −14
−4 −4
At the beginning of the problem the student made a distribution error. 4(1+5n) is equal to 4 + 20n as opposed to 4 + 5n.
A group of 8 friends bought tickets to Hershey Park, they also each bought a lemonade for $4.50. Another group of 3 friends also bought tickets to Hershey Park, they each bought a $10.00 gaming pass. This group also bought a locker for $15. If both groups spent the same amount which equation would represent the situation?
(Q16)
9(t+5)=4(t+12)+15
When you see "per" in a problem this usually means you need to do what?
Multiply a variable
(x – 10) – 0.25x = 0.5(3x + 6) – 4
(Q10)
x=12
The inverse of cubing
Cube root
2(x + 4) −8 = 3x +10− 4
2x +8−8 = 3x +6
2x = 3x +6
−3x −3x
x = 6
An error was made at the bottom. 2x – 3x is equal to –x as opposed to x.
Company A charges $15 per month for water delivery plus $2 per bottle. Company B charges $20 per month and $1.50 per bottle. After how many bottles will the total cost of both services be the same?
15+2b=20+1.50b
List three key words for addition and three key words for subtraction:
Possible answers for addition:
Add, plus, combine, total, heat, increase, additional, more, sum, all together, join, inn all, grow
Possible answer for subtraction:
Less, minus, take away, how many more, difference, decrease, cools, deduct, remain, left, fewer