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Let's solve the given system of equations and match them with their equivalent forms on the right side.

### First equation:
\[ 5x = 4 - 3x \]
Solve for \(x\):
\[
5x + 3x = 4
\]
\[
8x = 4
\]
\[
x = \frac{4}{8} = \frac{1}{2}
\]
Check the options: The equivalent equation is:
\[
2x = 4 \quad \text{(because when dividing both sides by 2, we get } x = \frac{1}{2} \text{)}
\]

### Second equation:
\[ 4x + 8 = 24 \]
Solve for \(x\):
\[
4x = 24 - 8
\]
\[
4x = 16
\]
\[
x = \frac{16}{4} = 4
\]
Check the options: The equivalent equation is:
\[
x + 2 = 6 \quad \text{(because } 4 + 2 = 6\text{)}
\]

### Third equation:
\[ 3x + 5 = 21x - 7 \]
Solve for \(x\):
\[
3x - 21x = -7 - 5
\]
\[
-18x = -12
\]
\[
x = \frac{-12}{-18} = \frac{2}{3}
\]
Check the options: The equivalent equation is:
\[
18x = 12 \quad \text{(when multiplied by 18, } x = \frac{2}{3} \text{)}
\]

### Final matching:
1. \( 5x = 4 - 3x \) is equivalent to \( 2x = 4 \)
2. \( 4x + 8 = 24 \) is equivalent to \( x + 2 = 6 \)
3. \( 3x + 5 = 21x - 7 \) is equivalent to \( 18x = 12 \)

Would you like more details or have any questions?

Here are five related questions:
1. How can we check if two equations are equivalent?
2. What are the steps to solve linear equations?
3. What does it mean for two equations to be equivalent in algebra?
4. How can simplifying equations help in finding equivalent forms?
5. What role does transposition of terms play in solving equations?

**Tip**: When solving linear equations, always aim to isolate the variable on one side of the equation to find its value more easily.

Welche Gleichungen sind äquivalent? Ordne die passenden Gleichungen zu.

Learn how to solve and match equivalent linear equations. This problem involves concepts of algebra, including solving linear equations by isolating variables and identifying equivalent equations through transformations. Suitable for students in Grades 7-9.

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