Algebra Class: Linear Equations and Functions

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).