Question

1.An expression for the length of the rectangle in terms of the width would be ________

2. The formula for the area of a rectangle is _______

3. Using trial and error, if the area is 96 m^2, then the length and width are _________

options:
1. L = 24 & w =4
2. L = 2w - 4
3. area = L x w
4. w = 2L - 4
5. area = 1 over (L x w)
6. area 2L + 2w
7. L = 4 & w = 24
8. L = 2 & w = 8
9. L = 8 & w = 12
10. L = 4 - 2w

Answer 1

Match the equation with its solution(s).

1. 3i + 2i − 7 = 18
2. 3i + 5 = 2i − 7
3. 3i + 5 = 3i + 7
4. 3(2i − 7) = 15
5. 3(2i + 7) = 6i + 21

options:

1. No solution
2. i = 6
3. i = 5
4. i = 2
5. i = 7
6. i = 11
7. i = -12
infinite solutions

Answer 2

1. An expression for the length of the rectangle in terms of the width would be **L = 2w - 4** (Option 2).

2. The formula for the area of a rectangle is **area = L x w** (Option 3).

3. Using trial and error, if the area is 96 m², then the length and width are **L = 8 & w = 12** (Option 9).

Answer 3

Let's solve each equation step by step and match them with their solutions.

1. **Equation:** \( 3i + 2i - 7 = 18 \)
**Solution:** Combine like terms: \( 5i - 7 = 18 \)
Add 7 to both sides: \( 5i = 25 \)
Divide by 5: \( i = 5 \)
**Match:** **i = 5** (Option 3)

2. **Equation:** \( 3i + 5 = 2i - 7 \)
**Solution:** Subtract \( 2i \) from both sides: \( i + 5 = -7 \)
Subtract 5 from both sides: \( i = -12 \)
**Match:** **i = -12** (Option 7)

3. **Equation:** \( 3i + 5 = 3i + 7 \)
**Solution:** Subtract \( 3i \) from both sides: \( 5 = 7 \)
This is a contradiction, so there is **no solution**.
**Match:** **No solution** (Option 1)

4. **Equation:** \( 3(2i - 7) = 15 \)
**Solution:** Expand: \( 6i - 21 = 15 \)
Add 21 to both sides: \( 6i = 36 \)
Divide by 6: \( i = 6 \)
**Match:** **i = 6** (Option 2)

5. **Equation:** \( 3(2i + 7) = 6i + 21 \)
**Solution:** Expand: \( 6i + 21 = 6i + 21 \)
This is an identity, which means it has **infinite solutions**.
**Match:** **infinite solutions** (Option 8)

### Summary of Matches:
1. \( 3i + 2i - 7 = 18 \) → **i = 5** (Option 3)
2. \( 3i + 5 = 2i - 7 \) → **i = -12** (Option 7)
3. \( 3i + 5 = 3i + 7 \) → **No solution** (Option 1)
4. \( 3(2i - 7) = 15 \) → **i = 6** (Option 2)
5. \( 3(2i + 7) = 6i + 21 \) → **infinite solutions** (Option 8)