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Questions and Answers
What is the value of x in the equation $4x - 8 = 0$?
What is the value of x in the equation $4x - 8 = 0$?
- 0
- 8
- 2 (correct)
- -2
Which operation is used to combine like terms in the expression $5x + 3x$?
Which operation is used to combine like terms in the expression $5x + 3x$?
- Adding (correct)
- Subtraction
- Dividing
- Multiplication
If two angles are supplementary and one angle measures $75°$, what is the measure of the other angle?
If two angles are supplementary and one angle measures $75°$, what is the measure of the other angle?
- 150°
- 75°
- 90°
- 105° (correct)
Which of the following describes vertical angles?
Which of the following describes vertical angles?
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When two parallel lines are cut by a transversal, how do the alternate interior angles relate to each other?
When two parallel lines are cut by a transversal, how do the alternate interior angles relate to each other?
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What is the simplified form of the expression $3(2x + 4) - 4x$?
What is the simplified form of the expression $3(2x + 4) - 4x$?
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Which of these statements is incorrect regarding angles?
Which of these statements is incorrect regarding angles?
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If $6x + 9 = 3(2x + 5)$, what is the solution for x?
If $6x + 9 = 3(2x + 5)$, what is the solution for x?
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What relationship exists between corresponding angles when a transversal intersects parallel lines?
What relationship exists between corresponding angles when a transversal intersects parallel lines?
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What is the result of simplifying the expression $4y - 2(2y - 3)$?
What is the result of simplifying the expression $4y - 2(2y - 3)$?
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Study Notes
Linear Equations in One Variable
- Definition: An equation that can be written in the form ax + b = 0, where a and b are constants, and x is the variable.
- Solution: To solve, isolate x by performing inverse operations.
- Example: For 3x + 6 = 0, subtract 6 from both sides, then divide by 3, giving x = -2.
Simple Algebra
- Basic Operations: Addition, subtraction, multiplication, and division of algebraic expressions.
- Like Terms: Terms that have the same variable raised to the same power can be combined.
- Distributive Property: a(b + c) = ab + ac.
- Example: Simplifying 2x + 3x = 5x.
Basic Fundamental Concepts
- Variables: Symbols (usually letters) that represent numbers.
- Constants: Fixed values that do not change.
- Expressions: Combinations of variables and constants using operations (e.g., 3x + 4).
- Equations: Statements that two expressions are equal.
Angles and its Properties
- Angle Definition: Formed by two rays with a common endpoint (vertex).
- Types of Angles:
- Acute: Less than 90°
- Right: Exactly 90°
- Obtuse: Greater than 90° but less than 180°
- Straight: Exactly 180°
- Angle Relationships:
- Complementary: Two angles that add up to 90°.
- Supplementary: Two angles that add up to 180°.
- Vertical angles: Opposite angles formed by two intersecting lines; they are equal.
Parallel Lines and Transversal Lines
- Parallel Lines: Lines in the same plane that never intersect; they have the same slope.
- Transversal Line: A line that intersects two or more lines at distinct points.
- Angle Relationships with Transversals:
- Corresponding Angles: Equal when a transversal crosses parallel lines.
- Alternate Interior Angles: Equal when a transversal crosses parallel lines.
- Same Side Interior Angles: Sum to 180° when a transversal crosses parallel lines.
Linear Equations in One Variable
- Linear equations are expressed in the form ax + b = 0, where a and b represent constants, and x is the variable to be solved.
- To find the value of x, perform inverse operations systematically to isolate x.
- For example, in the equation 3x + 6 = 0, subtracting 6 from both sides and dividing by 3 yields the solution x = -2.
Simple Algebra
- Basic arithmetic operations applied to algebraic expressions include addition, subtraction, multiplication, and division.
- Like terms can be added or subtracted, which are terms sharing the same variable raised to the same power.
- The Distributive Property states that a(b + c) can be expanded to ab + ac, facilitating simplification.
- An example of simplification is combining 2x and 3x to obtain 5x.
Basic Fundamental Concepts
- Variables are symbols (commonly letters) that stand in for unknown or changeable numbers.
- Constants are fixed numerical values that remain unchanged in expressions and equations.
- Algebraic expressions comprise variables and constants combined through arithmetic operations (e.g., 3x + 4).
- Equations assert that two expressions hold the same value, creating a statement of equality.
Angles and its Properties
- An angle consists of two rays extending from a common point called the vertex.
- Types of angles include:
- Acute: Angles measuring less than 90°.
- Right: Angles measuring exactly 90°.
- Obtuse: Angles measuring greater than 90° but less than 180°.
- Straight: Angles measuring exactly 180°.
- Angle relationships include:
- Complementary angles add to 90°.
- Supplementary angles add to 180°.
- Vertical angles, formed by intersecting lines, are always equal.
Parallel Lines and Transversal Lines
- Parallel lines reside in the same plane and will never meet, characterized by having equal slopes.
- A transversal is a line that crosses two or more lines at distinct intersection points.
- Key angle relationships with transversals include:
- Corresponding Angles: Equal in measure when a transversal intersects parallel lines.
- Alternate Interior Angles: Also equal when a transversal crosses two parallel lines.
- Same Side Interior Angles: Have a sum of 180° when intersected by a transversal across parallel lines.
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