Solving Equations and Inequalities Flashcard

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, greater than or equal to, or less than or equal to the other.

Front

How do you solve a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using inverse operations, such as addition, subtraction, multiplication, or division.

Front

What does it mean to isolate a variable in an equation?

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation 4x - 7 = 2x + 5?

Back

The solution is x = 6.

Front

What is the solution to the equation x^3 = 27?

Back

The solution is x = 3.

Front

How do you represent the solution of an inequality on a number line?

Back

To represent the solution of an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, and shade the appropriate region.

Front

What is the solution to the inequality 11x + 14 < -8?

Back

The solution is x < -2.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary value, while a non-strict inequality (≤ or ≥) includes the boundary value.

Front

What is the first step in solving the equation 5x - 9 = 3x + 7?

Back

The first step is to subtract 3x from both sides to begin isolating x.