Math worksheet for practicing evaluation of variable expressions with provided values.

Variable Expressions Worksheet Solution

We will solve each problem step by step, substituting the given values for the variables and simplifying the expressions.

---

#### 1a. $\frac{s + (-7)}{-1}$, when $s = -3$

1. Substitute $s = -3$ into the expression:
\[
\frac{s + (-7)}{-1} = \frac{-3 + (-7)}{-1}
\]
2. Simplify the numerator:
\[
-3 + (-7) = -3 - 7 = -10
\]
3. Divide by $-1$:
\[
\frac{-10}{-1} = 10
\]

Answer:
\[
\boxed{10}
\]

---

#### 1b. $(3 - (-4)x)^2$, when $x = 3$

1. Substitute $x = 3$ into the expression:
\[
(3 - (-4)x)^2 = (3 - (-4)(3))^2
\]
2. Simplify inside the parentheses:
\[
3 - (-4)(3) = 3 + 12 = 15
\]
3. Square the result:
\[
15^2 = 225
\]

Answer:
\[
\boxed{225}
\]

---

#### 2a. $w + (-7)$, when $w = -1$

1. Substitute $w = -1$ into the expression:
\[
w + (-7) = -1 + (-7)
\]
2. Simplify:
\[
-1 - 7 = -8
\]

Answer:
\[
\boxed{-8}
\]

---

#### 2b. $\frac{-4v}{c^2}$, when $v = -7$ and $c = -2$

1. Substitute $v = -7$ and $c = -2$ into the expression:
\[
\frac{-4v}{c^2} = \frac{-4(-7)}{(-2)^2}
\]
2. Simplify the numerator:
\[
-4(-7) = 28
\]
3. Simplify the denominator:
\[
(-2)^2 = 4
\]
4. Divide:
\[
\frac{28}{4} = 7
\]

Answer:
\[
\boxed{7}
\]

---

#### 3a. $-5d + (-6)u - 3$, when $d = 2$ and $u = 7$

1. Substitute $d = 2$ and $u = 7$ into the expression:
\[
-5d + (-6)u - 3 = -5(2) + (-6)(7) - 3
\]
2. Simplify each term:
\[
-5(2) = -10, \quad (-6)(7) = -42
\]
3. Combine the terms:
\[
-10 + (-42) - 3 = -10 - 42 - 3 = -55
\]

Answer:
\[
\boxed{-55}
\]

---

#### 3b. $q^2$, when $q = -10$

1. Substitute $q = -10$ into the expression:
\[
q^2 = (-10)^2
\]
2. Square $-10$:
\[
(-10)^2 = 100
\]

Answer:
\[
\boxed{100}
\]

---

#### 4a. $(10q - 4)^5$, when $q = 7$

1. Substitute $q = 7$ into the expression:
\[
(10q - 4)^5 = (10(7) - 4)^5
\]
2. Simplify inside the parentheses:
\[
10(7) - 4 = 70 - 4 = 66
\]
3. Raise to the power of 5:
\[
66^5
\]
(Note: This is a very large number, but the exact value is not typically simplified further in such problems unless specified.)

Answer:
\[
\boxed{66^5}
\]

---

#### 4b. $(5b - (-6))^2$, when $b = 0$

1. Substitute $b = 0$ into the expression:
\[
(5b - (-6))^2 = (5(0) - (-6))^2
\]
2. Simplify inside the parentheses:
\[
5(0) - (-6) = 0 + 6 = 6
\]
3. Square the result:
\[
6^2 = 36
\]

Answer:
\[
\boxed{36}
\]

---

#### 5a. $\frac{7p + 5}{-5}$, when $p = -3$

1. Substitute $p = -3$ into the expression:
\[
\frac{7p + 5}{-5} = \frac{7(-3) + 5}{-5}
\]
2. Simplify the numerator:
\[
7(-3) + 5 = -21 + 5 = -16
\]
3. Divide by $-5$:
\[
\frac{-16}{-5} = \frac{16}{5}
\]

Answer:
\[
\boxed{\frac{16}{5}}
\]

---

#### 5b. $\frac{6q - g}{4}$, when $q = -4$ and $g = 1$

1. Substitute $q = -4$ and $g = 1$ into the expression:
\[
\frac{6q - g}{4} = \frac{6(-4) - 1}{4}
\]
2. Simplify the numerator:
\[
6(-4) - 1 = -24 - 1 = -25
\]
3. Divide by 4:
\[
\frac{-25}{4}
\]

Answer:
\[
\boxed{-\frac{25}{4}}
\]

---

#### 6a. $q - r - (-1)$, when $q = 1$ and $r = 7$

1. Substitute $q = 1$ and $r = 7$ into the expression:
\[
q - r - (-1) = 1 - 7 - (-1)
\]
2. Simplify:
\[
1 - 7 - (-1) = 1 - 7 + 1 = -5
\]

Answer:
\[
\boxed{-5}
\]

---

#### 6b. $b - n - 8$, when $b = -3$ and $n = 5$

1. Substitute $b = -3$ and $n = 5$ into the expression:
\[
b - n - 8 = -3 - 5 - 8
\]
2. Simplify:
\[
-3 - 5 - 8 = -16
\]

Answer:
\[
\boxed{-16}
\]

---

#### 7a. $d(-7 - s)$, when $d = -5$ and $s = -2$

1. Substitute $d = -5$ and $s = -2$ into the expression:
\[
d(-7 - s) = -5(-7 - (-2))
\]
2. Simplify inside the parentheses:
\[
-7 - (-2) = -7 + 2 = -5
\]
3. Multiply:
\[
-5(-5) = 25
\]

Answer:
\[
\boxed{25}
\]

---

#### 7b. $p - c$, when $p = -3$ and $c = -8$

1. Substitute $p = -3$ and $c = -8$ into the expression:
\[
p - c = -3 - (-8)
\]
2. Simplify:
\[
-3 - (-8) = -3 + 8 = 5
\]

Answer:
\[
\boxed{5}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1a. & 10 \\
1b. & 225 \\
2a. & -8 \\
2b. & 7 \\
3a. & -55 \\
3b. & 100 \\
4a. & 66^5 \\
4b. & 36 \\
5a. & \frac{16}{5} \\
5b. & -\frac{25}{4} \\
6a. & -5 \\
6b. & -16 \\
7a. & 25 \\
7b. & 5 \\
\end{array}
}
\]