Multi-Step Equations

Front

What is a multi-step equation?

Back

A multi-step 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 if an equation has no solution?

Back

An equation has no solution when there are no values for the variable that can satisfy the equation. This often occurs when simplifying leads to a false statement, such as 0 = 5.

Front

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

Back

An equation has infinitely many solutions when any value for the variable satisfies the equation. This typically happens when both sides of the equation are equivalent after simplification.

Front

How do you solve the equation 8v - 4(v + 8) = 8?

Back

1. Distribute: 8v - 4v - 32 = 8 2. Combine like terms: 4v - 32 = 8 3. Add 32 to both sides: 4v = 40 4. Divide by 4: v = 10.

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 two or more terms inside a set of parentheses.

Front

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

Back

To determine this, simplify the equation. If you end up with a false statement (like 0 = 5), it has no solution. If you end up with a true statement (like 0 = 0), it has infinitely many solutions.

Front

Solve the equation 3x + 15 = 3(x + 5).

Back

1. Distribute: 3x + 15 = 3x + 15 2. Subtract 3x from both sides: 15 = 15. This is a true statement, so there are infinitely many solutions.

Front

What is the first step in solving the equation 3x - x + 2 = 4(2x - 1)?

Back

The first step is to simplify both sides of the equation. Distribute on the right side: 3x - x + 2 = 8x - 4.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, perform inverse operations to get the variable alone on one side of the equation. This may involve adding, subtracting, multiplying, or dividing both sides.

Front

What is the solution to the equation 4 - 6x - 2 = -2(3x - 1)?

Back

1. Simplify: 2 - 6x = -6x + 2 2. This simplifies to 2 = 2, which is always true. Therefore, there are infinitely many solutions.