Algebraic Expressions

Definition

Algebraic expressions are mathematical representations that combine variables, constants, and operations to express relationships and quantities. They are a fundamental component of algebra, used to model and solve a variety of problems involving unknown values.

5 Must Know Facts For Your Next Test

1. Algebraic expressions can be used to represent and solve problems involving the addition and subtraction of integers.
2. The properties of equality, such as the addition and subtraction properties, are essential in solving equations with algebraic expressions.
3. The division and multiplication properties of equality also play a crucial role in solving equations that contain algebraic expressions.
4. Algebraic expressions with variables and constants on both sides of an equation can be solved using various strategies, including isolating the variable.
5. Algebraic expressions are integral to solving linear inequalities, which involve comparing expressions to determine the range of values that satisfy the inequality.

Review Questions

• How can algebraic expressions be used to represent and solve problems involving the addition and subtraction of integers?
  • Algebraic expressions can be used to represent and solve problems involving the addition and subtraction of integers by assigning variables to unknown quantities and using the operations of addition and subtraction to model the relationships between the values. For example, an algebraic expression like $5x - 3$ could be used to represent a situation where a person has 5 times a certain number of items and 3 fewer items than that. The properties of equality, such as the addition and subtraction properties, can then be applied to solve for the unknown value represented by the variable $x$.
• Explain how the properties of equality, including the division and multiplication properties, are used to solve equations with algebraic expressions.
  • The properties of equality, such as the addition, subtraction, division, and multiplication properties, are essential in solving equations that contain algebraic expressions. These properties allow you to isolate the variable by performing the same operations on both sides of the equation, ensuring that the equality is maintained. For example, to solve an equation like $2x + 5 = 11$, you can first subtract 5 from both sides to isolate the variable term, then divide both sides by 2 to solve for $x$. The division and multiplication properties of equality are particularly important when dealing with algebraic expressions that involve variables with coefficients or when the variable appears on both sides of the equation.
• Analyze how algebraic expressions with variables and constants on both sides of an equation can be solved, and discuss the strategies used to isolate the variable.
  • Solving equations with algebraic expressions that have variables and constants on both sides requires a systematic approach to isolate the variable. This may involve combining like terms, using the properties of equality to move all the variable terms to one side and all the constant terms to the other side, and then applying the appropriate operation (addition, subtraction, multiplication, or division) to solve for the variable. For example, to solve an equation like $3x + 2 = 5x - 4$, you would first subtract $3x$ from both sides to isolate the variable terms, then subtract $5x$ from both sides to get $-2x = -6$, and finally divide both sides by $-2$ to solve for $x = 3$. The key is to methodically apply the properties of equality to manipulate the expression and isolate the variable.

Related terms

Variable:

A symbol, usually a letter, that represents an unknown or changeable quantity in an algebraic expression.

Constant:

A fixed value or quantity that does not change within the context of a particular expression or problem.

Coefficient:

A numerical value that multiplies a variable in an algebraic expression.