6th Grade Math: Variables and Equations

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.