Interpreting Equations
In the expression 5x + 7y − 32, what does the coefficient 5 represent if x is the number of pizzas sold?
The price/cost of the Pizza
Simplify:
x3⋅x4
x7
The formula for speed is s = d/t. What operation would you use to solve for d?
Multiplication, multiply both sides by t.
How many solutions does an equation have when both sides are completely different after simplifying?
No Solutions!
A student solves:
x + 5 = 12
x = 12 + 5
x = 17
What was the error made, what should have been done?
They should have subtracted 5 from both sides.
In the expression 2x + 3y = C, where C is the total cost, x is the number of waters and y is the number of chips; What does the term 3y represent?
The amount of chips and its cost/ the total for the chips
Simplify:
y8 / y3
y5
The formula for the area of a rectangle is A = lw. Solve for w.
A = lw
w = A / l
Solve for x:
7x − 3(x + 4) = 8
x=5
A student solves:
3x = 18
x = 18 -3
x = 15
What was the error made, what should have been done?
They should have divided both sides by 3
While planning for prom, Jenny made an expression including the amount of student tickets s, chaparone tickets c, and the rent for the venue.
She came up with 12s + 10c -120
What does 120 represent, and why is it being subtracted?
120 is the rent of the venue, they have to pay the venue.
Simplify:
(a4)2
a8
Using R = V/I, find R (resistance in ohms) when V = 240 volts and I = 12 amps.
R = 20 ohms
Solve for x:
3(2x + 1) = 6x − 4
No solutions!
A student solves:
2(x + 4) = 10
2x + 4 = 10
2x = 6
x=3
What was the error made, what should have been done?
They failed to distribute the 2 to both terms inside the parentheses
At the futbol game, if 10 student tickets (s) and 5 adult tickets (a) are sold, evaluate 8s + 12a − 45.
$95
Simplify:
x-3/x2
1/x5
The perimeter of a rectangle: P = 2L + 2w. Solve for L.
P = 2L + 2w
L = (P - 2w) / 2
2(3x + 1) − x = x + 2(x + 1)
Infinite Solutions!
A student solves:
5 - 2x = 13
-2x = 8
x = 4
What was the error made, what should have been done?
They forgot to divide by -2, so x=−4
A store sells pens for $1.50 and notebooks for $3.00. Write an equation for the total cost C of buying p pens and n notebooks.
C = 1.50p + 3n
Simplify completely:
(2x3y-2)2 / (4x4y-1)
x2 / y3
The formula d = rt (distance = rate × time). What is t if the distance is 10 meters and the rate is 2 meters per hour.
d = rt
5 hours
How many solutions does an equation have when both sides are identical after simplifying?
Infinite Solutions!
A student solves:
x/3 + 4 = 10
x + 4 =30
x = 26
What was the error made, what should have been done?
The student multiplied only the first term by 3; they should multiply every term, giving x+12=30, so x=18