Algebra Fundamentals: Solving Equations, Simplifying Express…

1. Solving Equations

• Linear Equation: Solve for $x$:$$3x + 7 = 22$$
• Quadratic Equation: Find the values of $x$:$$x^2 – 5x + 6 = 0$$
• System of Equations: Find the values of $x$ and $y$:$$begin{cases} 2x + y = 10 \ x – y = 2 end{cases}$$

2. Simplifying Expressions

• Combining Like Terms: Simplify the expression:$$4a + 5b – 2a + 3b – 7$$
• Distributive Property: Expand and simplify:$$3(2x – 4) + 5x$$
• Exponent Rules: Simplify the expression so it only contains positive exponents:$$frac{x^5 cdot x^{-2}}{x^2}$$

3. Analyzing Functions

• Linear Function (Slope): Find the slope and the y-intercept of the function:$$y = -2x + 4$$
• Domain and Range: Determine the domain of the following rational function:$$f(x) = frac{5}{x – 3}$$
• Function Evaluation: If $f(x) = 2x^2 – 3x + 1$, find the value of $f(4)$.