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 = c, where a, b, and c are constants.

Front

What is a linear inequality?

Back

A linear inequality is similar to a linear equation but uses inequality signs (>, <, ≥, ≤) instead of an equal sign. It represents a range of values rather than a single solution.

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 to isolate a variable?

Back

Isolating a variable means rearranging an 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 4 + x = 12?

Back

The solution is x = 8.

Front

How do you check if a solution is correct?

Back

To check if a solution is correct, substitute the solution back into the original equation and verify if both sides are equal.

Front

What is the solution to the inequality x > 5?

Back

The solution includes all real numbers greater than 5.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

What is the solution to the equation 2(x + 3) = 4?

Back

The solution is x = -1.

Front

What does the graph of a linear inequality look like?

Back

The graph of a linear inequality is a shaded region on one side of a boundary line, which represents all the solutions to the inequality.