Solving equations and inequalities

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 is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find the value(s) of the variable(s) that satisfy the inequality.

Front

What is the solution set of an equation?

Back

The solution set of an equation is the set of all values that satisfy the equation.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the difference between a closed dot and an open dot on a number line?

Back

A closed dot indicates that the number is included in the solution (≤ or ≥), while an open dot indicates that the number is not included ( < or >).

Front

What is the first step in solving the equation 250 + 65x = 575?

Back

Subtract 250 from both sides to isolate the term with the variable.

Front

What is the first step in solving the inequality 3x - 8 >= 7?

Back

Add 8 to both sides to begin isolating the variable.