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Questions and Answers
What makes an equation consist of?
What makes an equation consist of?
- Only one mathematical expression.
- Expressions on both sides separated by an inequality symbol.
- Two variables separated by an inequality symbol.
- Expressions on both sides separated by an equal sign. (correct)
Which method is not commonly used to solve both equations and inequalities?
Which method is not commonly used to solve both equations and inequalities?
- Graphing (correct)
- Multiplication/Division
- Addition/Subtraction
- Substitution
Which is a characteristic of a quadratic equation?
Which is a characteristic of a quadratic equation?
- The equation has a variable with a coefficient of 1.
- The highest power of the variable is 2. (correct)
- The highest power of the variable is 1.
- The equation has no variable.
What is typically the first step when using addition or subtraction to solve an equation?
What is typically the first step when using addition or subtraction to solve an equation?
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What is true about linear inequalities?
What is true about linear inequalities?
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Which type of equation is represented by $2x + 3 = 5$?
Which type of equation is represented by $2x + 3 = 5$?
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Which of the following changes the direction of the inequality symbol?
Which of the following changes the direction of the inequality symbol?
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Which variable value makes the quadratic equation $x^2 + 4x + 4 = 0$ true?
Which variable value makes the quadratic equation $x^2 + 4x + 4 = 0$ true?
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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.
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Description
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.
