Questions and Answers
What is the definition of variable?
An unknown amount, represented by a letter
What is the definition of coefficient?
A number that is multiplied by the variable
What is the definition of constant?
A number that stands alone (without a variable) in an expression
What is the definition of term?
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What is the definition of algebraic expression?
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What is the definition of numerical expression?
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What is the definition of inverse operation?
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What are the 6 steps to solve a shadow problem?
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Solve for x: 3x = -21.6
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Solve for x: -x/8 = 12
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Solve for x: 11.6 + 3x = -16.9
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Solve for x: x/9 - 7 = 3
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Solve for b: 2/3(9b - 7) = 36
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Solve for x: 0.5(2x - 4) = -17
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Solve for p: 14p - 8 = 22 + 20p
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Use the distributive property to write each expression as an equivalent equation: 13(10 - 7)
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Solve for x: (1.15 + 0.8x) = (2.3 - 1.5x)
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Solve for x: x/4 + 9 = 3x - (18 + 6)
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Supplementary angles are 2 angles in which the sum of their angle measures is ______ degrees.
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Complementary angles are 2 angles in which the sum of their angle measures is ______ degrees.
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Angles 1 and 2 are complementary angles. Angle 1 is 37 degrees, so what is the angle measure of angle 2?
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Angles 1 and 2 are supplementary angles. Angle 1 is 45 degrees, so what is the angle measure of angle 2?
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How do you check to prove that your answer to an algebra problem is correct?
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The sum of 3 consecutive integers is 72. Write and solve an equation to find the integers.
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The sum of 4 consecutive odd integers is 216. Write and solve an equation to find the integers.
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Study Notes
Definitions in Algebra
- Variable: An unknown amount shown by a letter in mathematical expressions.
- Coefficient: A numerical factor that multiplies the variable in an algebraic term.
- Constant: A standalone number without a variable in an expression.
- Term: A combination of constants and variables, typically linked with addition or subtraction.
- Algebraic Expression: Contains numbers, variables, and operators, but does not include an equals sign.
- Numerical Expression: Composed only of numbers and operators without any variables present.
- Inverse Operation: The process of applying the opposite mathematical operation to solve an equation.
Steps and Methods
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Steps to Solve a Shadow Problem:
- Create "L" shapes for clarity.
- Input known values.
- Establish a proportion.
- Cross-multiply, followed by a two-step solution for x.
- Substitute x back into the original equation to verify accuracy.
Solving Equations
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Equation Solutions:
- 3x = -21.6 results in x = -7.2
- -x/8 = 12 leads to x = -96
- 11.6 + 3x = -16.9 gives x = -9.5
- x/9 - 7 = 3 yields x = 20
- 2/3(9b - 7) resolves to b = 9
- 0.5(2x - 4) = -17 results in x = -15
- 14p - 8 = 22 + 20p gives p = -5
- (1.15 + 0.8x) = (2.3 - 1.5x) leads to x = 0.5
- x/4 + 9 = 3x - (18 + 6) solves for x = 12
Angles
- Supplementary Angles: Two angles that add up to 180 degrees.
- Complementary Angles: Two angles that sum to 90 degrees.
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Calculating Angles:
- If angle 1 is 37 degrees (complementary), angle 2 equals 53 degrees.
- If angle 1 measures 45 degrees (supplementary), angle 2 is 135 degrees.
Verification
- Checking Answers: Substitute the found value back into the original equation to confirm the solution is correct through computation.
Consecutive Integers Problems
- Three Consecutive Integers: Their combined sum is represented by the equation ((x+1) + x + (x-1) = 72).
- Four Consecutive Odd Integers: Formulated as ((x-2) + x + (x+2) + (x+4) = 216).
These highlights encapsulate essential algebraic concepts, problem-solving techniques, and angle relationships vital for understanding the topic.
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Test your knowledge of key algebra concepts including variables, coefficients, and algebraic expressions. This quiz also explores methods for solving equations and shadow problems. Perfect for reinforcing fundamental algebra techniques.