## Podcast Beta

## Questions and Answers

Solve for x: 2x + 5 = 17

x = 6

Simplify: 3(2x + 4) - 5

6x + 7

Solve for x: 4(x - 3) = 20

x = 8

Find the slope of the line passing through the points (2, 5) and (-3, 1)

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Solve for y: 2x + 3y = 9

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Simplify: 5x - 2(x - 3) + 4

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Find the solution to the system of equations: 2x + y = 8, x - y = 2

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Solve for x: 3(x + 2) = 15 - 2x

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Solve for x: 2x + 7 = 3x - 4

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Find the y-intercept of the line with equation y = 2x + 4

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Simplify: 2x^2 + 3x - 4x^2 + 5

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Solve for x: 3(x - 1) = 12

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## Study Notes

### Solving Linear Equations

- To solve (2x + 5 = 17), isolate x, resulting in (x = 6).
- The equation (3(2x + 4) - 5) simplifies to (6x + 7).
- From (4(x - 3) = 20), the solution is (x = 8).

### Slope Calculation

- The slope between points (2, 5) and (-3, 1) is calculated as ( \frac{1 - 5}{-3 - 2} = \frac{-4}{-5} = \frac{4}{5} ).

### Rearranging Equations

- The equation (2x + 3y = 9) can be rearranged to (y = \frac{9 - 2x}{3}).

### Simplifying Algebraic Expressions

- The expression (5x - 2(x - 3) + 4) simplifies to (3x + 10).
- The expression (2x^2 + 3x - 4x^2 + 5) results in (-2x^2 + 3x + 5).

### Systems of Equations

- For the system of equations (2x + y = 8) and (x - y = 2), the solution is (x = 3) and (y = 1).

### Solving for x

- The equation (3(x + 2) = 15 - 2x) simplifies to give (x = 1).
- The equation (2x + 7 = 3x - 4) leads to (x = 11).

### Finding Intercepts

- The y-intercept of the line (y = 2x + 4) is directly obtained as (4).

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## Description

This quiz covers fundamental concepts in algebra, including solving linear equations, calculating slopes, and simplifying algebraic expressions. It also addresses systems of equations and finding intercepts. Test your understanding of these crucial algebraic principles.