6th Grade Math: Variables and Equations

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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?

Dependent (correct)

Independent

Which variable is the independent variable in the number of hamburgers sold and the dollar amount of sales?

Dollar amount of sales

Number of hamburgers sold (correct)

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?

Dependent

Independent (correct)

Which variable is the dependent variable in the temperature of water and the number of minutes the water is in the freezer?

Temperature of water Signup and view all the answers

Identify the independent variable in the number of shelves in a bookcase and the number of books the bookcase can hold.

Number of shelves Signup and view all the answers

What is the solution of the equation x - 16 = 8?

x = 24 Signup and view all the answers

What is the solution of the equation 12 + x = 25?

x = 13 Signup and view all the answers

What is the solution of the equation x - 17 = 11?

x = 28 Signup and view all the answers

What is the solution of the equation x + 18 = 35?

x = 17 Signup and view all the answers

What is the solution of 7 = x - 28?

x = 35 Signup and view all the answers

What is the solution of the equation x - 12 = 40?

x = 52 Signup and view all the answers

What is the solution of the equation x - 12 = 13?

x = 25 Signup and view all the answers

What is the solution of the equation x + 8 = 40?

x = 32 Signup and view all the answers

What is the solution of the equation 34 = 16 + x?

x = 18 Signup and view all the answers

What is the solution of the equation x + 5 = 19?

x = 14 Signup and view all the answers

What is the solution of the equation 12 + x = 50?

x = 38 Signup and view all the answers

What is the solution of the equation x - 11 = 22?

x = 33 Signup and view all the answers

What is the solution of the equation x/25 = 4?

x = 100 Signup and view all the answers

What is the solution of the equation 18x = 18?

x = 1 Signup and view all the answers

What is the solution of the equation x/8 = 5?

x = 40 Signup and view all the answers

What is the solution of the equation 72 = 8x?

x = 9 Signup and view all the answers

What is the solution of the equation 12 = x/4?

x = 48 Signup and view all the answers

What is the solution of the equation 9 = x/3?

x = 27 Signup and view all the answers

What is the solution of the equation 150 = 3x?

x = 50 Signup and view all the answers

What is the solution of the equation 9x = 99?

x = 11 Signup and view all the answers

What is the value of 2x when x = 5?

10 Signup and view all the answers

What is the value of 2x - 5 when x = 3?

1 Signup and view all the answers

What is the value of 8c + 4 when c = 8?

68 Signup and view all the answers

What is the value of 10t when t = 9?

90 Signup and view all the answers

What is the equation for x if x = 2?

c/8 when c=16 Signup and view all the answers

Identify the inequality from the graph.

x > 5 Signup and view all the answers

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, isolate x by performing operations to both sides, resulting in x = 24.
Simple addition or subtraction yields results like 12 + x = 25 simplifies to x = 13.
Multiplication and division can also solve equations; for example, x/25 = 4 gives x = 100.

One-Step Multiplication and Division Equations

Equations such as 18x = 18 solve to x = 1 and highlight direct inverse relationships.
For division, x/8 = 5 results in x = 40, showing how to work with fractions effectively.

Algebra Substitution

Substitution involves replacing a variable within an equation. For example, 2x = 48 leads to x = 24.
Evaluating expressions by substituting known values results in straightforward calculations, like calculating 1 from 2x - 5 when x = 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 to x = 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 equals 12 = 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.