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?