Free worksheets for linear equations (grades 6-9, pre-algebra ... - Free Printable

Linear Equations Worksheet Solution

The task is to solve the given linear equations. Let's solve each equation step by step.

---

#### 1 a. \( 8 \cdot 5 = 4 + b \)

1. Simplify the left-hand side:
\[
8 \cdot 5 = 40
\]
So the equation becomes:
\[
40 = 4 + b
\]

2. Isolate \( b \) by subtracting 4 from both sides:
\[
40 - 4 = b
\]
\[
b = 36
\]

Solution:
\[
\boxed{36}
\]

---

#### 1 b. \( \frac{y}{11} = 9 \cdot 11 \)

1. Simplify the right-hand side:
\[
9 \cdot 11 = 99
\]
So the equation becomes:
\[
\frac{y}{11} = 99
\]

2. Eliminate the denominator by multiplying both sides by 11:
\[
y = 99 \cdot 11
\]
\[
y = 1089
\]

Solution:
\[
\boxed{1089}
\]

---

#### 2 a. \( 10 - 8 = \frac{p}{9} \)

1. Simplify the left-hand side:
\[
10 - 8 = 2
\]
So the equation becomes:
\[
2 = \frac{p}{9}
\]

2. Eliminate the denominator by multiplying both sides by 9:
\[
p = 2 \cdot 9
\]
\[
p = 18
\]

Solution:
\[
\boxed{18}
\]

---

#### 2 b. \( 2 + w = 8 \)

1. Isolate \( w \) by subtracting 2 from both sides:
\[
w = 8 - 2
\]
\[
w = 6
\]

Solution:
\[
\boxed{6}
\]

---

#### 3 a. \( 7 = 1 + w \)

1. Isolate \( w \) by subtracting 1 from both sides:
\[
w = 7 - 1
\]
\[
w = 6
\]

Solution:
\[
\boxed{6}
\]

---

#### 3 b. \( 1 = 10 - n \)

1. Isolate \( n \) by subtracting 10 from both sides:
\[
1 - 10 = -n
\]
\[
-9 = -n
\]

2. Multiply both sides by -1 to solve for \( n \):
\[
n = 9
\]

Solution:
\[
\boxed{9}
\]

---

#### 4 a. \( 1 + 7 = 4 + x \)

1. Simplify the left-hand side:
\[
1 + 7 = 8
\]
So the equation becomes:
\[
8 = 4 + x
\]

2. Isolate \( x \) by subtracting 4 from both sides:
\[
x = 8 - 4
\]
\[
x = 4
\]

Solution:
\[
\boxed{4}
\]

---

#### 4 b. \( w - 2 = 1 \cdot 11 \)

1. Simplify the right-hand side:
\[
1 \cdot 11 = 11
\]
So the equation becomes:
\[
w - 2 = 11
\]

2. Isolate \( w \) by adding 2 to both sides:
\[
w = 11 + 2
\]
\[
w = 13
\]

Solution:
\[
\boxed{13}
\]

---

Final Answers:

\[
\boxed{36, 1089, 18, 6, 6, 9, 4, 13}
\]