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Solutions
43 Videos

Solve using pencil and paper.

```
\displaystyle
x + 5 = 9
```

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Q1a

Solve using pencil and paper.

```
\displaystyle
f- 7 = 3
```

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Q1b

Solve using pencil and paper.

```
\displaystyle
3h = 15
```

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Q1c

Solve using pencil and paper.

```
\displaystyle
\frac{k}{4} = 3
```

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Q1d

Solve using a Computer Algebra System (CAS).

```
\displaystyle
2x + 5 = 11
```

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Q2a

Solve using a Computer Algebra System (CAS).

```
\displaystyle
3y - 5= -8
```

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Q2b

Solve using a Computer Algebra System (CAS).

```
\displaystyle
10+4f=-34
```

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Q2c

Solve using a Computer Algebra System (CAS).

```
\displaystyle
-5m -3= 12
```

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Q2d

Find the root of each equation using any method. Express fraction answers in lowest terms. Check each answer.

```
\displaystyle
5x + 2= 12
```

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Q3a

Find the root of each equation using any method. Express fraction answers in lowest terms. Check each answer.

```
\displaystyle
3p + 8 = 5
```

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Q3b

Find the root of each equation using any method. Express fraction answers in lowest terms. Check each answer.

```
\displaystyle
4 + 6w =2
```

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Q3c

```
\displaystyle
-6 + 4u = -3
```

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Q3d

John has $23.65 to spend on a book and magazines. The book costs $5.95. The magazines cost $2.95 each.

a) Write an equation that models the number of magazines that John can afford.

b) Solve the equation.

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Q4

Solve using pencil and paper.

`5x+4=2x+13`

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Q5a

Solve using pencil and paper.

`4c-3=2c+5`

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Q5b

Solve using pencil and paper.

`-3r+7=-5r-3`

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Q5c

Solve using pencil and paper.

`-6g-4=-3g+2`

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Q5d

Solve using a CAS.

`2a+5=6a+9`

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Q6a

Solve using a CAS.

`3b-7=b+5`

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Q6b

Solve using a CAS.

`5n+8=8n-10`

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Q6c

Solve using a CAS.

`-7d+3=-3d+11`

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Q6d

A triangle has angle measures that are related as follows:

The largest angle is 12 times the smallest angle.

The middle angle is 5 times the smallest angle.

Find the measures of the angles.

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Q7

Find the root of each equation using pencil and paper. Check each root.

`\dfrac{1}{2}(x+3)=5`

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Q8a

Find the root of each equation using pencil and paper. Check each root.

`\dfrac{b-5}{7}=3`

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Q8b

Find the root of each equation using pencil and paper. Check each root.

`6=\dfrac{2}{3}m-1`

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Q8c

Find the root of each equation using pencil and paper. Check each root.

`-5=\dfrac{3d+4}{3}`

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Q8d

Find the root of each equation using a CAS. Check each root.

`4=\dfrac{5r+7}{3}`

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Q9a

Find the root of each equation using a CAS. Check each root.

`\dfrac{1}{3}(p+5)=2p-3`

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Q9b

Find the root of each equation using a CAS. Check each root.

`3q+15=\dfrac{1}{2}(q-5)`

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Q9c

Find the root of each equation using a CAS. Check each root.

`\dfrac{2b+5}{4}=3`

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Q9d

Find the solution to each equation.

`\dfrac{x-5}{3}=\dfrac{x+4}{4}`

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Q10a

Find the solution to each equation.

`\dfrac{3}{4}(y-2)=\dfrac{2}{3}(y+1)`

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Q10b

Find the solution to each equation.

`\dfrac{b+5}{3}=\dfrac{b-3}{5}`

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Q10c

Find the solution to each equation.

`\dfrac{3}{5}(v+2)=\dfrac{1}{2}(v-3)`

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Q10d

Rearrange each formula to isolate the variable indicated.

`F=ma`

for `m`

(motion)

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Q11a

Rearrange each formula to isolate the variable indicated.

`V=IR`

for `I`

(voltage)

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Q11b

Rearrange each formula to isolate the variable indicated.

`A=\pi r^2`

for `r`

(area of a circle)

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Q11c

Rearrange each formula to isolate the variable indicated.

`P=2l+2w`

for `w`

(perimeter of a rectangle)

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Q11d

Rearrange each formula to isolate the variable indicated.

`y=mx+b`

for `x`

(linear relations)

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Q11e

The power, `P`

, in an electric circuit is related to the voltage, `V`

, and resistance, `R`

, by the formula `P=\dfrac{V^2}{R}`

.

a) Find the power, in watts (W), when the voltage is 100 V (volts) and the resistance is 50 `\Omega`

(ohms).

b) What is the resistance of a circuit that uses 100 W of power with a voltage of 20 V?

c) The resistance of a circuit is 15 `\Omega`

. The same circuit uses 60 W of power. Find the voltage in the circuit.

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Q12

The total of three cousinsâ€™ ages is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins?

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Q13

Adila sells T-shirts at a rock concert. She earns $8.00/h, plus $0.50 for each T-shirt she sells.

a) How much will Adila earn in a 4-h shift if she sells 35 T-shirts?

b) How many T-shirts must Adila sell to earn $80 in a 6-h shift?

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Q14

Ramesh sells hot dogs at a ball game. He earns $8.50/h, plus $0.35 for each hotdog he sells.

a) How much will Ramesh earn in a 4-h shift if he sells 52 hot dogs?

b) How many hot dogs must Ramesh sell to earn $103 in an 8-h shift?

c) How many hot dogs must Ramesh sell to earn $79 in a 6-h shift?

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Q15