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Questions and Answers
What is the definition of variable?
What is the definition of variable?
An unknown amount, represented by a letter
What is the definition of coefficient?
What is the definition of coefficient?
A number that is multiplied by the variable
What is the definition of constant?
What is the definition of constant?
A number that stands alone (without a variable) in an expression
What is the definition of term?
What is the definition of term?
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What is the definition of algebraic expression?
What is the definition of algebraic expression?
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What is the definition of numerical expression?
What is the definition of numerical expression?
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What is the definition of inverse operation?
What is the definition of inverse operation?
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What are the 6 steps to solve a shadow problem?
What are the 6 steps to solve a shadow problem?
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Solve for x: 3x = -21.6
Solve for x: 3x = -21.6
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Solve for x: -x/8 = 12
Solve for x: -x/8 = 12
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Solve for x: 11.6 + 3x = -16.9
Solve for x: 11.6 + 3x = -16.9
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Solve for x: x/9 - 7 = 3
Solve for x: x/9 - 7 = 3
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Solve for b: 2/3(9b - 7) = 36
Solve for b: 2/3(9b - 7) = 36
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Solve for x: 0.5(2x - 4) = -17
Solve for x: 0.5(2x - 4) = -17
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Solve for p: 14p - 8 = 22 + 20p
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)
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)
Solve for x: (1.15 + 0.8x) = (2.3 - 1.5x)
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Solve for x: x/4 + 9 = 3x - (18 + 6)
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.
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.
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?
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?
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?
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.
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.
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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Description
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.