Math worksheet for solving equations with algebraic expressions and decimals.

Problem: Solve the Equations

We are tasked with solving each equation and rounding the answers to the nearest hundredth. Let's solve each equation step by step.

---

#### 1) \( \frac{6.6 + y}{-6.2} = 2.5 \)

1. Multiply both sides by \(-6.2\) to eliminate the denominator:
\[
6.6 + y = 2.5 \times (-6.2)
\]
2. Calculate \( 2.5 \times (-6.2) \):
\[
2.5 \times (-6.2) = -15.5
\]
So,
\[
6.6 + y = -15.5
\]
3. Subtract 6.6 from both sides to isolate \( y \):
\[
y = -15.5 - 6.6
\]
4. Calculate \( -15.5 - 6.6 \):
\[
-15.5 - 6.6 = -22.1
\]
Therefore,
\[
y = -22.1
\]

Answer: \( y = -22.10 \)

---

#### 2) \( \frac{c - 4.4}{7.7} = 9.2 \)

1. Multiply both sides by 7.7 to eliminate the denominator:
\[
c - 4.4 = 9.2 \times 7.7
\]
2. Calculate \( 9.2 \times 7.7 \):
\[
9.2 \times 7.7 = 70.84
\]
So,
\[
c - 4.4 = 70.84
\]
3. Add 4.4 to both sides to isolate \( c \):
\[
c = 70.84 + 4.4
\]
4. Calculate \( 70.84 + 4.4 \):
\[
70.84 + 4.4 = 75.24
\]
Therefore,
\[
c = 75.24
\]

Answer: \( c = 75.24 \)

---

#### 3) \( \frac{d + 4.1}{-5.3} = -4.3 \)

1. Multiply both sides by \(-5.3\) to eliminate the denominator:
\[
d + 4.1 = -4.3 \times (-5.3)
\]
2. Calculate \( -4.3 \times (-5.3) \):
\[
-4.3 \times (-5.3) = 22.79
\]
So,
\[
d + 4.1 = 22.79
\]
3. Subtract 4.1 from both sides to isolate \( d \):
\[
d = 22.79 - 4.1
\]
4. Calculate \( 22.79 - 4.1 \):
\[
22.79 - 4.1 = 18.69
\]
Therefore,
\[
d = 18.69
\]

Answer: \( d = 18.69 \)

---

#### 4) \( \frac{4.8 - t}{-3.8} = 9.7 \)

1. Multiply both sides by \(-3.8\) to eliminate the denominator:
\[
4.8 - t = 9.7 \times (-3.8)
\]
2. Calculate \( 9.7 \times (-3.8) \):
\[
9.7 \times (-3.8) = -36.86
\]
So,
\[
4.8 - t = -36.86
\]
3. Subtract 4.8 from both sides to isolate \( -t \):
\[
-t = -36.86 - 4.8
\]
4. Calculate \( -36.86 - 4.8 \):
\[
-36.86 - 4.8 = -41.66
\]
So,
\[
-t = -41.66
\]
5. Multiply both sides by \(-1\) to solve for \( t \):
\[
t = 41.66
\]

Answer: \( t = 41.66 \)

---

#### 5) \( -6.8 - 4.8b = 5.6 \)

1. Add 6.8 to both sides to isolate the term with \( b \):
\[
-4.8b = 5.6 + 6.8
\]
2. Calculate \( 5.6 + 6.8 \):
\[
5.6 + 6.8 = 12.4
\]
So,
\[
-4.8b = 12.4
\]
3. Divide both sides by \(-4.8\) to solve for \( b \):
\[
b = \frac{12.4}{-4.8}
\]
4. Calculate \( \frac{12.4}{-4.8} \):
\[
\frac{12.4}{-4.8} \approx -2.5833
\]
Rounding to the nearest hundredth:
\[
b \approx -2.58
\]

Answer: \( b = -2.58 \)

---

#### 6) \( -7.7n - 6.7 = 9.2 \)

1. Add 6.7 to both sides to isolate the term with \( n \):
\[
-7.7n = 9.2 + 6.7
\]
2. Calculate \( 9.2 + 6.7 \):
\[
9.2 + 6.7 = 15.9
\]
So,
\[
-7.7n = 15.9
\]
3. Divide both sides by \(-7.7\) to solve for \( n \):
\[
n = \frac{15.9}{-7.7}
\]
4. Calculate \( \frac{15.9}{-7.7} \):
\[
\frac{15.9}{-7.7} \approx -2.0649
\]
Rounding to the nearest hundredth:
\[
n \approx -2.06
\]

Answer: \( n = -2.06 \)

---

#### 7) \( -4.2 + \frac{6}{7}a = 8.9 \)

1. Add 4.2 to both sides to isolate the term with \( a \):
\[
\frac{6}{7}a = 8.9 + 4.2
\]
2. Calculate \( 8.9 + 4.2 \):
\[
8.9 + 4.2 = 13.1
\]
So,
\[
\frac{6}{7}a = 13.1
\]
3. Multiply both sides by \( \frac{7}{6} \) to solve for \( a \):
\[
a = 13.1 \times \frac{7}{6}
\]
4. Calculate \( 13.1 \times \frac{7}{6} \):
\[
13.1 \times \frac{7}{6} = 13.1 \times 1.1667 \approx 15.3333
\]
Rounding to the nearest hundredth:
\[
a \approx 15.33
\]

Answer: \( a = 15.33 \)

---

#### 8) \( \frac{k - 9.8}{-9.3} = 7.7 \)

1. Multiply both sides by \(-9.3\) to eliminate the denominator:
\[
k - 9.8 = 7.7 \times (-9.3)
\]
2. Calculate \( 7.7 \times (-9.3) \):
\[
7.7 \times (-9.3) = -71.61
\]
So,
\[
k - 9.8 = -71.61
\]
3. Add 9.8 to both sides to isolate \( k \):
\[
k = -71.61 + 9.8
\]
4. Calculate \( -71.61 + 9.8 \):
\[
-71.61 + 9.8 = -61.81
\]
Therefore,
\[
k = -61.81
\]

Answer: \( k = -61.81 \)

---

#### 9) \( \frac{4.9 + r}{4.6} = 7.1 \)

1. Multiply both sides by 4.6 to eliminate the denominator:
\[
4.9 + r = 7.1 \times 4.6
\]
2. Calculate \( 7.1 \times 4.6 \):
\[
7.1 \times 4.6 = 32.66
\]
So,
\[
4.9 + r = 32.66
\]
3. Subtract 4.9 from both sides to isolate \( r \):
\[
r = 32.66 - 4.9
\]
4. Calculate \( 32.66 - 4.9 \):
\[
32.66 - 4.9 = 27.76
\]
Therefore,
\[
r = 27.76
\]

Answer: \( r = 27.76 \)

---

#### 10) \( \frac{1}{3}z - 4.8 = 6.2 \)

1. Add 4.8 to both sides to isolate the term with \( z \):
\[
\frac{1}{3}z = 6.2 + 4.8
\]
2. Calculate \( 6.2 + 4.8 \):
\[
6.2 + 4.8 = 11.0
\]
So,
\[
\frac{1}{3}z = 11.0
\]
3. Multiply both sides by 3 to solve for \( z \):
\[
z = 11.0 \times 3
\]
4. Calculate \( 11.0 \times 3 \):
\[
11.0 \times 3 = 33.0
\]
Therefore,
\[
z = 33.0
\]

Answer: \( z = 33.00 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \ y = -22.10 \\
2) & \ c = 75.24 \\
3) & \ d = 18.69 \\
4) & \ t = 41.66 \\
5) & \ b = -2.58 \\
6) & \ n = -2.06 \\
7) & \ a = 15.33 \\
8) & \ k = -61.81 \\
9) & \ r = 27.76 \\
10) & \ z = 33.00 \\
\end{aligned}
}
\]