https://file.aiquickdraw.com/mathbot/file/17268863751059vw1lds6.jpg

The image contains three linear equations to solve, each involving a single variable. Here are the solutions for each equation:

### 1. Solve the following linear equations:

#### a) \( 3x = -24 \)

**Solution:**
Divide both sides by 3 to isolate \( x \):
\[
x = \frac{-24}{3}
\]
\[
x = -8
\]

#### b) \( 7z + 56 = -z \)

**Solution:**
First, move all terms involving \( z \) to one side by adding \( z \) to both sides:
\[
7z + z + 56 = 0
\]
\[
8z + 56 = 0
\]
Subtract 56 from both sides:
\[
8z = -56
\]
Divide by 8:
\[
z = \frac{-56}{8}
\]
\[
z = -7
\]

#### c) \( 14x + 3 = 45 \)

**Solution:**
Subtract 3 from both sides:
\[
14x = 45 - 3
\]
\[
14x = 42
\]
Divide by 14:
\[
x = \frac{42}{14}
\]
\[
x = 3
\]

### Final Answers:
a) \( x = -8 \)  
b) \( z = -7 \)  
c) \( x = 3 \)

Would you like a detailed explanation of any specific step, or do you have any other questions?

### Related Questions:
1. How do you solve multi-step linear equations?
2. What are some common mistakes to avoid when solving linear equations?
3. How can you check your solutions for linear equations?
4. What happens when there are no solutions to a linear equation?
5. How do you solve equations involving fractions or decimals?

### Tip:
Always double-check your work by substituting your solution back into the original equation to verify that it holds true!

Solve the following linear equalities in one variable:
a) 3x = -24
b) 7z + 56 = -z
c) 14x + 3 = 45

Learn how to solve basic linear equations, including examples like 3x = -24 and 14x + 3 = 45, using algebraic techniques. Suitable for students in Grades 6-8. Detailed step-by-step solutions provided.

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