Flashcard # 1: Solving linear equations and inequalities in one variable

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = 0, where a and b are constants.

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. Examples include x > 5 or x ≤ 3.

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 (addition, subtraction, multiplication, division) until the variable is alone.

Front

What does it mean for an equation to have infinite solutions?

Back

An equation has infinite solutions when any value of the variable satisfies the equation, often occurring when both sides of the equation are equivalent.

Front

What is the solution to the inequality 5x - 3 > 2?

Back

x > 1.

Front

What is the first step in solving the equation 12x - 14x + 2 = 20 - 6?

Back

Combine like terms: -2x + 2 = 14.

Front

What is the solution to the equation 3x + 9 = 2x + 9?

Back

x = 0.

Front

How do you graph the solution of an inequality?

Back

To graph the solution of an inequality, use a number line. Use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate side.

Front

What is the solution to the inequality x > 5?

Back

Any number greater than 5 is a solution, such as 6, 7, or 10.

Front

What is the purpose of using the TI Nspire for solving equations?

Back

The TI Nspire helps to perform calculations, visualize graphs, and solve equations efficiently using its built-in functions.