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

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. 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.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable that makes the equation true.

Front

What does it mean to solve a linear inequality?

Back

To solve a linear inequality means to find the range of values for the variable that makes the inequality true.

Front

What is the solution set of an inequality?

Back

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

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line, then shade the region that satisfies the inequality.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

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

Back

Combine like terms on both sides of the equation.

Front

What is the solution to the inequality -4x + 14 ≤ 54?

Back

x ≥ -10.

Front

What does 'h ≥ 48' represent in the context of height restrictions?

Back

It means that a person must be at least 48 inches tall to ride.