Expressions and Equations Analysis

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing one or more variables.

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they have the same value for all values of the variables involved.

Front

How do you solve the equation 6x = 78?

Back

To solve for x, divide both sides by 6: x = 78 / 6 = 13.

Front

What is a variable in mathematics?

Back

A variable is a symbol, often a letter, that represents a number in an equation or expression.

Front

What is a linear expression?

Back

A linear expression is an algebraic expression in which each term is either a constant or the product of a constant and a single variable.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

What is a coefficient?

Back

A coefficient is a numerical factor in a term of an algebraic expression, such as the 5 in 5x.

Front

How do you write an expression for a total cost that includes a flat fee and a variable cost?

Back

The expression is written as: Total Cost = Flat Fee + (Variable Cost per unit * Number of units).

Front

What is the purpose of simplifying an expression?

Back

Simplifying an expression makes it easier to understand and solve, reducing it to its most basic form.

Front

What does it mean to evaluate an expression?

Back

To evaluate an expression means to calculate its value by substituting the variables with specific numbers.