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Algebra Practice Sheet
Introduction
Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating those symbols. In algebra, we use letters or symbols to represent numbers and quantities in equations and formulas.
What is an Equation?
An equation is a mathematical statement that two expressions are equal. An equation is written using an equal sign (=) and can be solved by finding the value of the unknown variable.
Example:
2x + 3 = 7
In this equation, the unknown variable is x. To solve this equation, we need to find the value of x.
Solution:
2x + 3 = 7
2x = 4
x = 2
What is an Inequality?
An inequality is a mathematical statement that two expressions are not equal. An inequality is written using an inequality sign ( >, <, ≥, or ≤) and can be solved by finding the value of the unknown variable.
Example:
2x + 3 > 7
In this inequality, the unknown variable is x. To solve this inequality, we need to find the value of x.
Solution:
2x + 3 > 7
2x > 4
x > 2
What is a Linear Equation?
A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are constants and x is the variable. Linear equations can be solved by using the addition, subtraction, multiplication, and division properties of equality.
Example:
2x + 3 = 7
In this equation, a = 2, b = 3, and c = 7. To solve this equation, we need to find the value of x.
Solution:
2x + 3 = 7
2x = 4
x = 2
What is a Quadratic Equation?
A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are constants and x is the variable. Quadratic equations can be solved by using the quadratic formula or by completing the square.
Example:
2x2 + 5x - 3 = 0
In this equation, a = 2, b = 5, and c = -3. To solve this equation, we need to find the value of x.
Solution:
Using the quadratic formula:
x = (-5 ± √(25 - 4(2)(-3))/2(2)
x = (-5 ± √49)/4
x = (-5 ± 7)/4
x = -1 or 2
