https://file.aiquickdraw.com/mathbot/file/1725966722800pjynu3cd.jpg

Let's go through these problems one by one:

### 1. Simplify each of these algebraic expressions.

**a**: \( 3x + 5a - 5x + 2a \)
- Combine like terms: \( (3x - 5x) + (5a + 2a) \)
- Simplified: \( -2x + 7a \)

**b**: \( 3(x + y) - 2(3x - y) \)
- Distribute: \( 3x + 3y - 6x + 2y \)
- Combine like terms: \( (3x - 6x) + (3y + 2y) \)
- Simplified: \( -3x + 5y \)

**c**: \( 2ab - 5bc + 3ab + 7cb \)
- Combine like terms: \( (2ab + 3ab) + (-5bc + 7cb) \)
- Simplified: \( 5ab + 2bc \)

**d**: \( -2x \times 4y + 5xy \)
- Multiply: \( -8xy + 5xy \)
- Simplified: \( -3xy \)

**e**: \( \frac{45x^2w^2}{15xw^3} \)
- Cancel common factors: \( \frac{45}{15} \times \frac{x^2}{x} \times \frac{w^2}{w^3} \)
- Simplified: \( 3x \times \frac{1}{w} = \frac{3x}{w} \)

**f**: \( \frac{169a^b^2c^3}{13a^3b^2c} \)
- Cancel common factors: \( \frac{169}{13} \times \frac{a^b^2c^3}{a^3b^2c} \)
- Simplified: \( 13a^{b^2}/\4 ^  ____ .. "" @path

Simplify algebraic expressions, solve algebraic equations, inequalities, and factorize expressions from the given image.

This problem set covers algebraic expressions, equations, inequalities, and geometry, focusing on simplifying expressions, solving equations, graphing inequalities, and calculating perimeter and area. Suitable for students in Grades 7-9.

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