Simplifying Algebraic Expressions worksheet with six practice problems.

The image you provided contains a worksheet titled "Simplifying Algebraic Expressions." The task is to simplify the given algebraic expressions. Below, I will solve each problem step by step and explain the process.

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Problem 1:

$$
5x + 3y - 2x + 4y
$$

#### Step-by-Step Solution:
1. Identify like terms:
- Terms involving \( x \): \( 5x \) and \( -2x \)
- Terms involving \( y \): \( 3y \) and \( 4y \)

2. Combine like terms:
- For \( x \)-terms: \( 5x - 2x = 3x \)
- For \( y \)-terms: \( 3y + 4y = 7y \)

3. Write the simplified expression:
$$
3x + 7y
$$

#### Final Answer:
$$
\boxed{3x + 7y}
$$

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Problem 2:

$$
8a - 4b + 6a - 3b
$$

#### Step-by-Step Solution:
1. Identify like terms:
- Terms involving \( a \): \( 8a \) and \( 6a \)
- Terms involving \( b \): \( -4b \) and \( -3b \)

2. Combine like terms:
- For \( a \)-terms: \( 8a + 6a = 14a \)
- For \( b \)-terms: \( -4b - 3b = -7b \)

3. Write the simplified expression:
$$
14a - 7b
$$

#### Final Answer:
$$
\boxed{14a - 7b}
$$

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Problem 3:

$$
7m - 2n + 3m + 5n
$$

#### Step-by-Step Solution:
1. Identify like terms:
- Terms involving \( m \): \( 7m \) and \( 3m \)
- Terms involving \( n \): \( -2n \) and \( 5n \)

2. Combine like terms:
- For \( m \)-terms: \( 7m + 3m = 10m \)
- For \( n \)-terms: \( -2n + 5n = 3n \)

3. Write the simplified expression:
$$
10m + 3n
$$

#### Final Answer:
$$
\boxed{10m + 3n}
$$

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Problem 4:

$$
9p - 6q - 4p + 2q
$$

#### Step-by-Step Solution:
1. Identify like terms:
- Terms involving \( p \): \( 9p \) and \( -4p \)
- Terms involving \( q \): \( -6q \) and \( 2q \)

2. Combine like terms:
- For \( p \)-terms: \( 9p - 4p = 5p \)
- For \( q \)-terms: \( -6q + 2q = -4q \)

3. Write the simplified expression:
$$
5p - 4q
$$

#### Final Answer:
$$
\boxed{5p - 4q}
$$

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Problem 5:

$$
4r + 7s - 3r - 2s
$$

#### Step-by-Step Solution:
1. Identify like terms:
- Terms involving \( r \): \( 4r \) and \( -3r \)
- Terms involving \( s \): \( 7s \) and \( -2s \)

2. Combine like terms:
- For \( r \)-terms: \( 4r - 3r = r \)
- For \( s \)-terms: \( 7s - 2s = 5s \)

3. Write the simplified expression:
$$
r + 5s
$$

#### Final Answer:
$$
\boxed{r + 5s}
$$

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Problem 6:

$$
6t - 5u + 2t + 3u
$$

#### Step-by-Step Solution:
1. Identify like terms:
- Terms involving \( t \): \( 6t \) and \( 2t \)
- Terms involving \( u \): \( -5u \) and \( 3u \)

2. Combine like terms:
- For \( t \)-terms: \( 6t + 2t = 8t \)
- For \( u \)-terms: \( -5u + 3u = -2u \)

3. Write the simplified expression:
$$
8t - 2u
$$

#### Final Answer:
$$
\boxed{8t - 2u}
$$

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Summary of Answers:

1. \( \boxed{3x + 7y} \)
2. \( \boxed{14a - 7b} \)
3. \( \boxed{10m + 3n} \)
4. \( \boxed{5p - 4q} \)
5. \( \boxed{r + 5s} \)
6. \( \boxed{8t - 2u} \)

These are the simplified forms of the given algebraic expressions. If you have any further questions, feel free to ask!