Linear Equation Worksheets (printable, online, answers, examples) - Free Printable

Problem Description:

The task involves solving one-step equations with integers. The worksheet provides a set of equations and asks for their solutions. Below is the list of equations to solve:

1. \( 3 + x = -13 \)
2. \( -4m = 55 \)
3. \( 0 = 2x - 7 \)
4. \( y - 1 = -5 \)
5. \( \frac{p}{6} = 9 \)
6. \( 78k = -3 \)
7. \( -6 + m = -1.2 \)

Solution Approach:

To solve each equation, we will isolate the variable on one side of the equation using basic algebraic operations (addition, subtraction, multiplication, or division). Let's solve each equation step by step.

---

#### Equation 1: \( 3 + x = -13 \)

1. Subtract 3 from both sides to isolate \( x \):
\[
3 + x - 3 = -13 - 3
\]
\[
x = -16
\]

Solution: \( x = -16 \)

---

#### Equation 2: \( -4m = 55 \)

1. Divide both sides by \(-4\) to isolate \( m \):
\[
\frac{-4m}{-4} = \frac{55}{-4}
\]
\[
m = -\frac{55}{4}
\]

Solution: \( m = -\frac{55}{4} \)

---

#### Equation 3: \( 0 = 2x - 7 \)

1. Add 7 to both sides to isolate the term with \( x \):
\[
0 + 7 = 2x - 7 + 7
\]
\[
7 = 2x
\]

2. Divide both sides by 2 to solve for \( x \):
\[
\frac{7}{2} = \frac{2x}{2}
\]
\[
x = \frac{7}{2}
\]

Solution: \( x = \frac{7}{2} \)

---

#### Equation 4: \( y - 1 = -5 \)

1. Add 1 to both sides to isolate \( y \):
\[
y - 1 + 1 = -5 + 1
\]
\[
y = -4
\]

Solution: \( y = -4 \)

---

#### Equation 5: \( \frac{p}{6} = 9 \)

1. Multiply both sides by 6 to isolate \( p \):
\[
6 \cdot \frac{p}{6} = 9 \cdot 6
\]
\[
p = 54
\]

Solution: \( p = 54 \)

---

#### Equation 6: \( 78k = -3 \)

1. Divide both sides by 78 to isolate \( k \):
\[
\frac{78k}{78} = \frac{-3}{78}
\]
\[
k = -\frac{3}{78}
\]

2. Simplify the fraction:
\[
k = -\frac{1}{26}
\]

Solution: \( k = -\frac{1}{26} \)

---

#### Equation 7: \( -6 + m = -1.2 \)

1. Add 6 to both sides to isolate \( m \):
\[
-6 + m + 6 = -1.2 + 6
\]
\[
m = 4.8
\]

Solution: \( m = 4.8 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad x = -16 \\
2. & \quad m = -\frac{55}{4} \\
3. & \quad x = \frac{7}{2} \\
4. & \quad y = -4 \\
5. & \quad p = 54 \\
6. & \quad k = -\frac{1}{26} \\
7. & \quad m = 4.8
\end{aligned}
}
\]