One Solution, No Solution, Infinite Solutions

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that there are countless values of the variable that satisfy the equation, often because the equation simplifies to a true statement (e.g., 0 = 0).

Front

What does it mean if an equation has no solution?

Back

It means that there are no values of the variable that can satisfy the equation, often because it simplifies to a false statement (e.g., 0 = 5).

Front

What is an example of an equation with infinitely many solutions?

Back

3x + 15 = 3(x + 5) simplifies to 0 = 0.

Front

What is an example of an equation with no solution?

Back

2x + 1 = 2x - 1 simplifies to 1 = -1.

Front

How can you identify if an equation has one solution?

Back

If the equation simplifies to a statement where the variable can be isolated to a single value (e.g., x = 2).

Front

What is the first step in solving linear equations?

Back

Combine like terms and simplify both sides of the equation.

Front

What does the term 'like terms' refer to?

Back

Terms in an expression that have the same variable raised to the same power.

Front

What is the significance of the distributive property in solving equations?

Back

It allows you to multiply a single term by each term inside a parenthesis, helping to simplify equations.

Front

What is the solution to the equation 3(x-2) + 1 = 3x - 5?

Back

Infinitely Many Solutions.

Front

What is the solution to the equation 6x + 9 - x = 3x + 9 + x?

Back

No Solution.