Questions and Answers
Is w the dependent or independent variable in the context of the pages P in a book and the weight, w of the book?
Which variable is the independent variable in the number of hamburgers sold and the dollar amount of sales?
Is p the dependent or independent variable in the context of the pounds of flour you buy and the number of bread loaves you want to make?
Which variable is the dependent variable in the temperature of water and the number of minutes the water is in the freezer?
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Identify the independent variable in the number of shelves in a bookcase and the number of books the bookcase can hold.
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What is the solution of the equation x - 16 = 8?
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What is the solution of the equation 12 + x = 25?
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What is the solution of the equation x - 17 = 11?
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What is the solution of the equation x + 18 = 35?
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What is the solution of 7 = x - 28?
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What is the solution of the equation x - 12 = 40?
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What is the solution of the equation x - 12 = 13?
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What is the solution of the equation x + 8 = 40?
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What is the solution of the equation 34 = 16 + x?
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What is the solution of the equation x + 5 = 19?
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What is the solution of the equation 12 + x = 50?
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What is the solution of the equation x - 11 = 22?
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What is the solution of the equation x/25 = 4?
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What is the solution of the equation 18x = 18?
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What is the solution of the equation x/8 = 5?
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What is the solution of the equation 72 = 8x?
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What is the solution of the equation 12 = x/4?
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What is the solution of the equation 9 = x/3?
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What is the solution of the equation 150 = 3x?
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What is the solution of the equation 9x = 99?
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What is the value of 2x when x = 5?
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What is the value of 2x - 5 when x = 3?
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What is the value of 8c + 4 when c = 8?
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What is the value of 10t when t = 9?
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What is the equation for x if x = 2?
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Identify the inequality from the graph.
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Study Notes
Dependent and Independent Variables
- Dependent variables are affected by independent variables, for instance, the weight of a book depends on the number of pages.
- Independent variables can be controlled or changed, such as the number of hamburgers sold which affects total sales.
- When examining relationships, if one variable changes the other is dependent on that change.
Solving 1-Step Equations
- In solving equations like
x - 16 = 8
, isolatex
by performing operations to both sides, resulting inx = 24
. - Simple addition or subtraction yields results like
12 + x = 25
simplifies tox = 13
. - Multiplication and division can also solve equations; for example,
x/25 = 4
givesx = 100
.
One-Step Multiplication and Division Equations
- Equations such as
18x = 18
solve tox = 1
and highlight direct inverse relationships. - For division,
x/8 = 5
results inx = 40
, showing how to work with fractions effectively.
Algebra Substitution
- Substitution involves replacing a variable within an equation. For example,
2x = 48
leads tox = 24
. - Evaluating expressions by substituting known values results in straightforward calculations, like calculating
1
from2x - 5
whenx = 3
.
Inequalities
- Inequalities indicate a range of values and can represent relationships graphically, e.g.,
x > 5
signifies all numbers greater than 5. - Understanding the notation and symbol applications is crucial for grasping algebraic expressions involving ranges.
Practice with Equations and Solutions
- Various equations are provided to practice solving and identifying relationships, such as
7 = x - 28
solving tox = 35
. - Equations presented include both positive and negative solutions emphasizing different mathematical approaches.
Summary of Key Values
- Several integers and solutions appear throughout the material, reflecting outcomes of equations that enhance understanding of algebraic principles.
- Values include notable integers like
48
, which equals12 = x/4
, illustrating direct relationships in algebraic contexts.
Conclusion on Math Concepts
- Mastery of independent and dependent variables is essential for algebraic problem-solving.
- Understanding how to manipulate and solve 1-step equations through addition, subtraction, multiplication, and division fosters stronger math skills.
- Inequalities and practices related to substitution lay groundwork for advanced mathematical concepts and critical thinking, crucial for higher-level mathematics.
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Description
Test your knowledge on dependent and independent variables, and practice solving one-step equations in this 6th-grade math quiz. Explore topics like substitution and inequalities through engaging flashcards that reinforce key algebra concepts.