8 Questions
What makes an equation consist of?
Expressions on both sides separated by an equal sign.
Which method is not commonly used to solve both equations and inequalities?
Graphing
Which is a characteristic of a quadratic equation?
The highest power of the variable is 2.
What is typically the first step when using addition or subtraction to solve an equation?
Isolate the constants on one side.
What is true about linear inequalities?
The highest power of the variable is 1.
Which type of equation is represented by $2x + 3 = 5$?
Linear Equation
Which of the following changes the direction of the inequality symbol?
Multiplying or dividing both sides by a negative value.
Which variable value makes the quadratic equation $x^2 + 4x + 4 = 0$ true?
x = -2
Study Notes
Equations
- An equation is a statement that says two mathematical expressions are equal.
- It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).
- The goal is to find the value of the variable(s) that makes the equation true.
Types of Equations:
- Simple Equations: Equations in which the variable has a coefficient of 1, e.g., 2x = 5.
- Linear Equations: Equations in which the highest power of the variable is 1, e.g., 2x + 3 = 5.
- Quadratic Equations: Equations in which the highest power of the variable is 2, e.g., x^2 + 4x + 4 = 0.
Methods for Solving Equations:
- Addition/Subtraction: Add or subtract the same value to both sides of the equation to isolate the variable.
- Multiplication/Division: Multiply or divide both sides of the equation by the same non-zero value to isolate the variable.
- Substitution: Substitute a value or expression into the equation to solve for the variable.
Inequalities
- An inequality is a statement that says two mathematical expressions are not equal.
- It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an inequality symbol (<, >, ≤, ≥).
- The goal is to find the range of values that makes the inequality true.
Types of Inequalities:
- Linear Inequalities: Inequalities in which the highest power of the variable is 1, e.g., 2x + 3 > 5.
- Quadratic Inequalities: Inequalities in which the highest power of the variable is 2, e.g., x^2 + 4x + 4 > 0.
Methods for Solving Inequalities:
- Addition/Subtraction: Add or subtract the same value to both sides of the inequality to isolate the variable.
- Multiplication/Division: Multiply or divide both sides of the inequality by the same non-zero value, but be careful with the direction of the inequality symbol.
- Graphing: Graph the related function and find the range of values that makes the inequality true.
Note: When solving inequalities, the direction of the inequality symbol changes when multiplying or dividing by a negative value.
Equations
- An equation is a statement that says two mathematical expressions are equal.
- It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).
- The goal is to find the value of the variable(s) that makes the equation true.
Types of Equations
- Simple Equations: equations in which the variable has a coefficient of 1, e.g., 2x = 5.
- Linear Equations: equations in which the highest power of the variable is 1, e.g., 2x + 3 = 5.
- Quadratic Equations: equations in which the highest power of the variable is 2, e.g., x^2 + 4x + 4 = 0.
Methods for Solving Equations
- Addition/Subtraction: add or subtract the same value to both sides of the equation to isolate the variable.
- Multiplication/Division: multiply or divide both sides of the equation by the same non-zero value to isolate the variable.
- Substitution: substitute a value or expression into the equation to solve for the variable.
Inequalities
- An inequality is a statement that says two mathematical expressions are not equal.
- It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an inequality symbol (, ≤, ≥).
- The goal is to find the range of values that makes the inequality true.
Types of Inequalities
- Linear Inequalities: inequalities in which the highest power of the variable is 1, e.g., 2x + 3 > 5.
- Quadratic Inequalities: inequalities in which the highest power of the variable is 2, e.g., x^2 + 4x + 4 > 0.
Methods for Solving Inequalities
- Addition/Subtraction: add or subtract the same value to both sides of the inequality to isolate the variable.
- Multiplication/Division: multiply or divide both sides of the inequality by the same non-zero value, but be careful with the direction of the inequality symbol.
- Graphing: graph the related function and find the range of values that makes the inequality true.
- Note: when solving inequalities, the direction of the inequality symbol changes when multiplying or dividing by a negative value.
Learn about the basics of equations and their types, including simple and linear equations. Understand how to find the value of variables that makes the equation true.
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