11 Questions
What is the first step in solving for x in the equation 2x + 3 = 5?
Isolate the variable x on one side of the equation by subtracting 3 from both sides.
What is the quadratic formula used to solve quadratic equations?
x = (-b ± √(b^2 - 4ac)) / 2a
What is the process of expressing an algebraic expression as a product of simpler expressions called?
Factorizing
How do you simplify the expression 2x^2 + 4x?
Factor out the greatest common factor (GCF) of 2x, which gives 2x(x + 2).
What is the formula for the difference of squares?
a^2 - b^2 = (a + b)(a - b)
How do you simplify the expression (2x^2 + 4x) / 2x?
Cancel out the common factor of 2x, which gives x + 2.
Solve for x in the equation $x/2 + 2 = 7$.
x = 10
Factorize the expression $3x^2 + 6x$.
$3x(x + 2)$
Simplify the expression $5x - 3 + 2x + 2$.
$7x - 1$
Solve for x in the equation $2x - 3 = 11$.
x = 7
Simplify the expression $(3x^2 + 6x) / 3x$.
$x + 2$
Study Notes
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.
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