Multistep Equations - Variables on Both Sides

Front

What is a multistep equation?

Back

A multistep equation is an equation that requires more than one step to solve. It often involves combining like terms, using the distributive property, and isolating the variable.

Front

What does it mean when an equation has infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation. This typically occurs when both sides of the equation simplify to the same expression.

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when there is no value for the variable that can make the equation true. This often happens when the equation simplifies to a false statement, such as 0 = 5.

Front

How do you solve the equation 2x - x + 7 = x + 3 + 4?

Back

Combine like terms: x + 7 = x + 7. Since both sides are equal, the equation has infinite solutions.

Front

How do you solve the equation -2(x + 1) = -2x + 5?

Back

Distribute: -2x - 2 = -2x + 5. Adding 2x to both sides gives -2 = 5, which is false. Therefore, there is no solution.

Front

How do you solve the equation -2(x + 1) = 2(x - 1)?

Back

Distribute: -2x - 2 = 2x - 2. Adding 2 to both sides gives -2x = 0, so x = 0.

Front

What is the solution to the equation 2x + 2x + 2 = 4x + 2?

Back

Combine like terms: 4x + 2 = 4x + 2. Since both sides are equal, the equation has infinite solutions.

Front

How do you solve the equation 12 + 2x - x = 9x + 6?

Back

Combine like terms: 12 + x = 9x + 6. Rearranging gives 6 = 8x, so x = \frac{3}{4}.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term inside a set of parentheses.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, while 3x and 4y are not.