Let's solve each problem step by step from the
Variable Expressions Worksheet.
---
1 a.
$$
\frac{s + (-7)}{-1}, \text{ when } s = -3
$$
Substitute $ s = -3 $:
$$
\frac{-3 + (-7)}{-1} = \frac{-10}{-1} = 10
$$
✔ Answer: 10
---
1 b.
$$
(3 - (-4)x)^2, \text{ when } x = 3
$$
First simplify inside the parentheses:
$$
3 - (-4)(3) = 3 + 12 = 15
$$
Now square it:
$$
15^2 = 225
$$
✔ Answer: 225
---
2 a.
$$
w + (-7), \text{ when } w = -1
$$
$$
-1 + (-7) = -8
$$
✔ Answer: -8
---
2 b.
$$
\frac{-4v}{c^2}, \text{ when } v = -7, c = -2
$$
First compute $ c^2 $:
$$
(-2)^2 = 4
$$
Now plug in values:
$$
\frac{-4(-7)}{4} = \frac{28}{4} = 7
$$
✔ Answer: 7
---
3 a.
$$
-5d + (-6)u - 3, \text{ when } d = 2, u = 7
$$
Substitute:
$$
-5(2) + (-6)(7) - 3 = -10 - 42 - 3 = -55
$$
✔ Answer: -55
---
3 b.
$$
q^2, \text{ when } q = -10
$$
$$
(-10)^2 = 100
$$
✔ Answer: 100
---
4 a.
$$
(10q - 4)^5, \text{ when } q = 7
$$
Compute inside:
$$
10(7) - 4 = 70 - 4 = 66
$$
Now raise to 5th power:
$$
66^5 = \text{Very large number}
$$
But let's calculate it step by step:
- $ 66^2 = 4356 $
- $ 66^3 = 66 \times 4356 = 287,496 $
- $ 66^4 = 66 \times 287,496 = 18,974,736 $
- $ 66^5 = 66 \times 18,974,736 = 1,252,332,576 $
✔ Answer: 1,252,332,576
---
4 b.
$$
(5b - (-6))^2, \text{ when } b = 0
$$
Simplify:
$$
5(0) - (-6) = 0 + 6 = 6
$$
Then square:
$$
6^2 = 36
$$
✔ Answer: 36
---
5 a.
$$
\frac{7p + 5}{-5}, \text{ when } p = -3
$$
Substitute:
$$
\frac{7(-3) + 5}{-5} = \frac{-21 + 5}{-5} = \frac{-16}{-5} = \frac{16}{5} = 3.2
$$
✔ Answer: $ \frac{16}{5} $ or $ 3.2 $
---
5 b.
$$
\frac{6q - g}{4}, \text{ when } q = -4, g = 1
$$
Substitute:
$$
\frac{6(-4) - 1}{4} = \frac{-24 - 1}{4} = \frac{-25}{4} = -6.25
$$
✔ Answer: $ -\frac{25}{4} $ or $ -6.25 $
---
6 a.
$$
q - r - (-1), \text{ when } q = 1, r = 7
$$
$$
1 - 7 - (-1) = -6 + 1 = -5
$$
✔ Answer: -5
---
6 b.
$$
b - n - 8, \text{ when } b = -3, n = 5
$$
$$
-3 - 5 - 8 = -16
$$
✔ Answer: -16
---
7 a.
$$
d(-7 - s), \text{ when } d = -5, s = -2
$$
First compute inside the parentheses:
$$
-7 - (-2) = -7 + 2 = -5
$$
Now multiply:
$$
-5 \times (-5) = 25
$$
✔ Answer: 25
---
7 b.
$$
p - c, \text{ when } p = -3, c = -8
$$
$$
-3 - (-8) = -3 + 8 = 5
$$
✔ Answer: 5
---
✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1a | 10 |
| 1b | 225 |
| 2a | -8 |
| 2b | 7 |
| 3a | -55 |
| 3b | 100 |
| 4a | 1,252,332,576 |
| 4b | 36 |
| 5a | $ \frac{16}{5} $ or 3.2 |
| 5b | $ -\frac{25}{4} $ or -6.25 |
| 6a | -5 |
| 6b | -16 |
| 7a | 25 |
| 7b | 5 |
Let me know if you'd like these answers formatted into a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of evaluating algebraic expressions worksheet.
