Understanding Linear Equations in One Variable

The video tutorial explains how to solve linear equations in one variable, highlighting that while typically one solution is expected, equations can also have infinite solutions or no solutions. The first example shows an equation with infinite solutions, where both sides simplify to the same expression. The second example demonstrates an equation with no solutions, where simplification leads to a false statement. The tutorial emphasizes understanding these outcomes when solving linear equations.

What is the typical expectation when solving a linear equation in one variable?

• One solution

• Infinite solutions

• Two solutions

• No solutions

What does it mean if both sides of a linear equation simplify to the same expression?

• The equation has no solutions

• The equation has one solution

• The equation is unsolvable

• The equation has infinite solutions

What is the significance of the equation -18 = -18 in the context of solutions?

• It indicates a mistake

• It indicates no solutions

• It indicates one solution

• It indicates infinite solutions

What is the result when variable terms on both sides of an equation cancel out?

• The equation has one solution

• The equation has infinite solutions

• The equation has no solutions

• The equation is unsolvable

What is the first step in solving a multi-step linear equation?

• Add a constant to both sides

• Clear the parentheses

• Divide both sides by a constant

• Multiply both sides by a variable

In the second example, what operation is performed to simplify the left side of the equation?

• Subtracting 6X

• Adding 6X

• Multiplying by 7

• Distributing negative 3

What does it indicate if the resulting equation is false after simplifying?

• The equation has infinite solutions

• The equation has one solution

• The equation is incorrect

• The equation has no solutions

What does DNE stand for in the context of solutions?

• Does Not Equal

• Does Not End

• Does Not Evaluate

• Does Not Exist

What is the outcome if a simplified equation results in a false statement?

• The equation has one solution

• The equation has infinite solutions

• The equation has no solutions

• The equation is incorrect

What are the possible outcomes when solving a linear equation in one variable?

• Only one solution

• Only infinite solutions

• One solution, no solutions, or infinite solutions

• Only no solutions