Chapter 6: Expanding the Equation:
Introducing Variables
In algebra, variables are symbols that represent unknown or
changeable quantities. They are foundational to understanding
and working with equations on a more complex level. This
chapter explores the role of variables in algebra, how to
construct and solve two-step equations, and introduces
algebraic expressions.
More on Variables and How They Are Used in
Algebra
Variables, typically represented by letters such as \( x \), \( y \),
and \( z \), are used to stand in for unknown numbers. They
allow mathematicians and students to formulate equations and
expressions that can solve a wide range of problems. For
example, in the equation \( x + 5 = 10 \), \( x \) is a variable
representing the number that, when added to 5, equals 10.
Constructing and Solving Two-Step Equations
Two-step equations are slightly more complex than one-step
equations because they require two operations to solve. For
instance, in the equation \( 2x + 3 = 11 \), you need to perform
two operations to isolate \( x \) and solve the equation:
1. Subtract 3 from both sides to get \( 2x = 8 \).
2. Divide both sides by 2 to find \( x = 4 \).
Introducing Variables
In algebra, variables are symbols that represent unknown or
changeable quantities. They are foundational to understanding
and working with equations on a more complex level. This
chapter explores the role of variables in algebra, how to
construct and solve two-step equations, and introduces
algebraic expressions.
More on Variables and How They Are Used in
Algebra
Variables, typically represented by letters such as \( x \), \( y \),
and \( z \), are used to stand in for unknown numbers. They
allow mathematicians and students to formulate equations and
expressions that can solve a wide range of problems. For
example, in the equation \( x + 5 = 10 \), \( x \) is a variable
representing the number that, when added to 5, equals 10.
Constructing and Solving Two-Step Equations
Two-step equations are slightly more complex than one-step
equations because they require two operations to solve. For
instance, in the equation \( 2x + 3 = 11 \), you need to perform
two operations to isolate \( x \) and solve the equation:
1. Subtract 3 from both sides to get \( 2x = 8 \).
2. Divide both sides by 2 to find \( x = 4 \).
