Determining Solutions to Equations

What is the first step in solving an equation with one solution?

• Multiply both sides by a constant

• Divide both sides by a variable

• Subtract a variable from both sides

• Add a constant to both sides

In an equation with one solution, what is the next step after removing a variable from both sides?

• Combine like terms

• Isolate the remaining variable

• Add a variable to both sides

• Subtract a constant from both sides

When solving for an equation, what does adding the same number to both sides accomplish?

• It proves the equation has no solution

• It eliminates the variable from the equation

• It helps to isolate the variable

• It changes the equation's solution

What does it mean when an equation has one solution?

• The equation is balanced with no variables

• The equation simplifies to a single variable equal to a number

• The variables cancel out completely

• The equation cannot be simplified

What happens to the variables in an equation with no solution?

• They are eliminated from both sides

• They are added to both sides

• They are subtracted from both sides

• They remain unchanged

What does it mean when after simplification, the constants on both sides of an equation are not equal?

• The equation has infinite solutions

• The equation has no solution

• The equation is incorrectly formed

• The equation has one solution

How can you tell if an equation has no solution?

• Both sides of the equation are identical

• The variables are the same but the constants are different after simplification

• The constants on both sides are equal after simplification

• The variables on both sides are different

What indicates an equation has an infinite number of solutions?

• One side of the equation is a constant, and the other is a variable

• Both sides of the equation are completely identical

• The variables are eliminated, leaving unequal constants

• The variables and constants are different on both sides

What is a characteristic of an equation that simplifies to an identity?

• It has a variable equal to a constant

• It simplifies to a contradiction

• It indicates the equation has no solution

• It shows the equation has infinite solutions

What is the result of simplifying an equation with infinite solutions?

• An identity, showing all real numbers are solutions

• A new equation with different variables

• A contradiction, indicating no solution

• A specific number that the variable equals