Solve for the unknown.
a) \displaystyle
8 + m = - 2
b) \displaystyle
k - 7 = -11
c) \displaystyle
3x = 18
d) \displaystyle
\frac{h}{5} = -4
Find the root of each question.
a) \displaystyle
2y - 7 = 13
b) \displaystyle
4 + 5v = -21
Find the root of each question.
a) \displaystyle
9 - 2x = -1
b) \displaystyle
-3s - 6 = 9
Find the root.
a) \displaystyle
3n + 8 = 20
b) \displaystyle
9 -4r = - 27
c) \displaystyle
5x - 2 = 18
d) \displaystyle
-7y - 6 = -20
Cindy has $2.50 to spend on milk and candy. The milk costs $0.70. Her favourite candies cost $0.12 each.
a) Write an equation that models the number of candies that Cindy can afford.
b) Solve the equation.
Solve using pencil and paper.
\displaystyle
3 + 2n + 6m = 19
Solve using pencil and paper.
\displaystyle
72 - 4 + 2 + 12 = 0
Solve using pencil and paper.
\displaystyle
3x + 7 = 2x - 3
Solve using pencil and paper.
\displaystyle
5w - 6 = -4w + 3
Solve using pencil and paper.
\displaystyle
5 + 5y = 2y + 9
Solve using pencil and paper.
\displaystyle
7 + 3k - 2= 4k
Solve using pencil and paper.
\displaystyle
2w-9 + 5w + 2 =0
Solve using pencil and paper.
\displaystyle
-5 + 7n = 9n + 11
Find p.
\displaystyle
4 - (3p -2) = p - 10
Find h.
\displaystyle
3 + (h -2) = 5 + 3h
Find n.
\displaystyle
2(n - 8) = -4(2n -1)
Find n.
\displaystyle
3(2k - 5) -k = 4 -(3k + 7)
A triangle has angle measures that are related as follows:
• the largest angle is eight times the smallest angle
• the middle angle is triple the smallest angle
Find the measures of the angles.
Find the root of the equation using pencil and paper.
\displaystyle
\frac{1}{3}(x - 1) =4
Find the root of the equation using pencil and paper.
\displaystyle
\frac{b -4}{3} = -5
Find the root of the equation using pencil and paper.
\displaystyle
3 = \frac{3}{4}(p - 1)
Find the root of the equation using pencil and paper.
\displaystyle
-3 = \frac{5x + 4}{7}
Find the root of the equation using pencil and paper.
\displaystyle
7 = \frac{6q + 8}{4}
Find the root of the equation using pencil and paper.
\displaystyle
\frac{1}{2}(u -5) = 2u + 5
Find the root of the equation using pencil and paper.
\displaystyle
\frac{y- 8}{3} = \frac{y + 4}{2}
Find the root of the equation using pencil and paper.
\displaystyle
\frac{2}{3}(w - 5) = \frac{3}{4}(w+ 2)
Find the root of the equation using pencil and paper.
\displaystyle
\frac{c + 3}{4} = \frac{c - 5}{6}
Find the root of the equation using pencil and paper.
\displaystyle
\frac{2}{5}(x + 3) = \frac{1}{2}(x - 5)
Rearrange each formula to isolate the variable indicated.
P = a + b + c for a
Rearrange each formula to isolate the variable indicated.
C = \pi d for d
Rearrange each formula to isolate the variable indicated.
a = \frac{F }{m} for F
Rearrange each formula to isolate the variable indicated.
d = mt + b for t
The power, P, in an electric circuit is related to the current, I, and resistance, R, by the formula P = I^2R.
a) Find the power, in watts (W), when the current is 0.5 A (amperes) and the resistance is 600 \Omega (ohms).
b) What is the resistance of a circuit that uses 500 W of power with a current of 2 A?
c) The resistance in a circuit is 4 \displaystyle \Omega . The same circuit uses 100 W of power. Find the current in the circuit.
The total of three sisters’ ages is 39. Dina is half as old as Michelle and 3 years younger than Juliette. How old are the sisters?
Sven sells hamburgers at a ballpark. He earns $7.50/h, plus $0.40 for each hamburger he sells.
a) How much will Sven earn in a 3-h shift if he sells 24 hamburgers?
b) How many hamburgers must Sven sell to earn $100 in a 6.5-h shift?
Hitori’s rock garden is in the shape of a trapezoid. The garden has an area of 60 m2 and a depth of 8 m. The front width is double the back width.
Without changing the front or back widths, by how much must Hitori increase the depth of his garden to double its area?