Equations and Inequalities

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables and constants, and is often solved to find the value of the variables.

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does it mean for two angles to be congruent?

Back

Two angles are congruent if they have the same measure.

Front

How do you solve for x in the equation 5x + 24 = 9x - 17?

Back

To solve for x, first rearrange the equation: 5x - 9x = -17 - 24, which simplifies to -4x = -41. Then, divide both sides by -4 to find x = 10.25.

Front

What is the purpose of using inequalities in real-life situations?

Back

Inequalities are used to represent situations where there are limits or constraints, such as budget constraints, minimum requirements, or comparisons between different options.

Front

How do you represent a total cost with an equation?

Back

A total cost can be represented with an equation by adding fixed costs to variable costs, such as Total Cost = Fixed Cost + (Variable Cost per item × Number of items).

Front

What is the significance of the slope in a linear equation?

Back

The slope of a linear equation represents the rate of change of the dependent variable with respect to the independent variable, indicating how steep the line is.

Front

How can you determine the minimum number of items to purchase to stay within a budget using inequalities?

Back

You can set up an inequality that compares the total cost of items to the budget and solve for the variable representing the number of items.

Front

What is a variable in an equation?

Back

A variable is a symbol, often represented by letters, that stands for an unknown value in an equation or expression.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging an equation so that the variable is on one side of the equation by itself, making it easier to solve.