Algebra Basics: Solving Equations and Simplifying

What is the first step in solving for x in the equation 2x + 3 = 5?

What is the quadratic formula used to solve quadratic equations?

What is the process of expressing an algebraic expression as a product of simpler expressions called?

How do you simplify the expression 2x^2 + 4x?

What is the formula for the difference of squares?

How do you simplify the expression (2x^2 + 4x) / 2x?

Solve for x in the equation $x/2 + 2 = 7$.

Factorize the expression $3x^2 + 6x$.

Simplify the expression $5x - 3 + 2x + 2$.

Solve for x in the equation $2x - 3 = 11$.

Simplify the expression $(3x^2 + 6x) / 3x$.

Solving for x

Linear Equations: To solve for x, isolate the variable x on one side of the equation by adding, subtracting, multiplying, or dividing both sides by the same value.
- Example: 2x + 3 = 5 → 2x = 5 - 3 → 2x = 2 → x = 2/2 → x = 1
Quadratic Equations: Can be solved using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
- Example: x^2 + 4x + 4 = 0 → x = (-4 ± √(4^2 - 4(1)(4))) / 2(1) → x = (-4 ± √(16 - 16)) / 2 → x = (-4 ± √0) / 2 → x = -4 / 2 → x = -2

Factorizing

Factorizing is the process of expressing an algebraic expression as a product of simpler expressions.
Factor out the greatest common factor (GCF) of the terms:
- Example: 2x^2 + 4x = 2x(x + 2)
Factorize quadratic expressions of the form ax^2 + bx + c:
- Example: x^2 + 5x + 6 = (x + 2)(x + 3)
Difference of Squares: a^2 - b^2 = (a + b)(a - b)
- Example: x^2 - 4 = (x + 2)(x - 2)

Simplifying

Simplify algebraic expressions by combining like terms:
- Example: 2x + 3x = 5x
Simplify expressions by canceling out common factors:
- Example: (2x^2 + 4x) / 2x = x + 2
Simplify rational expressions by canceling out common factors between the numerator and denominator:
- Example: (2x + 4) / (x + 2) = 2

Learn how to solve linear and quadratic equations, factorize algebraic expressions, and simplify rational expressions. Understand the steps to isolate variables and cancel out common factors.