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Solutions
23 Videos

Use a graph to determine the solution to each equation.

a) `x + 2= 7`

b) `4x - 4 = 8`

c) `-2x -9= -5`

d) `-7x -14 = -14`

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Q1

A submarine starts at sea level and descends 50 m every 5 min.

a) Make a table of values of the submarine’s depth. Use intervals of5 min, up to 30 min.

b) Graph the submarine’s depth at 30 min.

c) What patterns do you see in the table and the graph?

d) If the submarine started at a depth of 219 m, what relation would model the submarine's location in relation to time?

e) Create an equation to show how long it would take the submarine to reach a depth of 428 m.

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Q2

Solve using inverse operations.

`2x - 5 = 7`

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Q3a

Solve using inverse operations.

`3x + 4 = 10`

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Q3b

Solve using inverse operations.

`-6 = 3 + 3x`

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Q3c

Solve using inverse operations.

`-2.1k + 5.6 = 20.2`

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Q3d

Solve using inverse operations.

`-8.75z + 12.5 = 12.5`

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Q3e

Solve using inverse operations.

`-a + 5 = 0`

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Q3f

Anna joins a book club. The first six books are free, but after that he pays $8.98 per book.

a) Write an expression for the cost of `b`

books.

b) How much would he pay for eight books?

c) Anna receives his first shipment of books with a bill for $53.88. Create and solve an equation to determine how many books he ordered.

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Q4

Solve for `x`

.

```
\displaystyle
-x + 6 = 2x - 12
```

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Q5a

Solve for `x`

.

```
\displaystyle
\frac{2}{3}x - 2 = 4x + \frac{4}{3}
```

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Q5b

Solve for `x`

.

```
\displaystyle
4(x - 8) = -2(x - 5)
```

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Q5c

Solve for `x`

.

```
\displaystyle
\frac{2}{3}x -\frac{1}{2} = -\frac{1}{2} + \frac{1}{4}x
```

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Q5d

Solve for `x`

.

```
\displaystyle
\frac{1}{5}(x+1) = \frac{1}{3}(2x - 3)
```

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Q5e

Solve for `x`

.

```
\displaystyle
\frac{4x- 2}{5} + \frac{1}{2} = \frac{3x + 7}{2} - 1
```

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Q5f

For each equation, write an equivalent equation multiply both sides by a constant to eliminate fraction expression then solve.

```
\displaystyle
\frac{k}{3} + 1 = 4
```

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Q6a

For each equation, write an equivalent equation multiply both sides by a constant to eliminate fraction expression then solve.

```
\displaystyle
\frac{x}{2} - 3 = 1\frac{1}{6}
```

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Q6b

For each equation, write an equivalent equation multiply both sides by a constant to eliminate fraction expression then solve.

```
\displaystyle
-1\frac{2}{3}g + \frac{7}{9} = 0
```

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Q6c

```
\displaystyle
\frac{2}{3}h + \frac{1}{4} = 3\frac{1}{2}
```

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Q6d

Create and solve an equation to answer each problem below.

The perimeter of a rectangle is 210 m. The length is 7 m longer than the width.

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Q7a

Solve for `x`

.

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Q7b

Tom has 117 quarters and dimes worth a total of `\$15.75`

. How many of each coin does he have?

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Q7c

Jim can paint a house in `10`

h and Mandy can paint the same house in `12`

h. How long will it take if they work together?

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Q7d