Multi Step Equations (one, many, no solution)

Front

What is a multi-step equation?

Back

An equation that requires more than one step to solve, often involving operations like addition, subtraction, multiplication, and division.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that will satisfy the equation.

Front

What is an example of an equation with no solution?

Back

3(2x + 1) = 6x + 1, which simplifies to 6x + 3 = 6x + 1, leading to a false statement.

Front

What is an infinitely many solutions scenario?

Back

When an equation simplifies to a true statement for all values of the variable, such as 2(x + 5) = 2x + 10.

Front

How do you solve the equation 3x + 2(4x - 4) = 3?

Back

1. Distribute: 3x + 8x - 8 = 3. 2. Combine like terms: 11x - 8 = 3. 3. Add 8: 11x = 11. 4. Divide by 11: x = 1.

Front

What is the first step in solving the equation 5 - 2(x - 7) = x + 1 + 3x?

Back

You cannot perform '5 - 2' first; you should distribute -2 to (x - 7) first.

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value for the variable that satisfies the equation.

Front

How do you determine if an equation has one solution, no solution, or infinitely many solutions?

Back

By simplifying the equation and analyzing the resulting statements for contradictions or identities.

Front

What is the solution to the equation 5x - 2 = 3?

Back

x = 1.

Front

What is the solution set for the equation 2(x + 5) = 2x + 5?

Back

No solution, as it simplifies to a false statement.