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 is the first step to solve the equation 10 + 2x = 16?

Back

Subtract 10 from both sides to isolate the term with the variable: 2x = 6.

Front

What is the solution to the equation 2x = 6?

Back

Divide both sides by 2 to find x: x = 3.

Front

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

Back

First, distribute -4: 8v - 4v - 32 = 8. Then combine like terms: 4v - 32 = 8. Finally, add 32 to both sides and divide by 4: v = 10.

Front

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

Back

It means that any value for the variable will satisfy the equation, often occurring when both sides of the equation are equivalent after simplification.

Front

What is the solution to the equation 3x + 15 = 3(x + 5)?

Back

Both sides simplify to the same expression, indicating infinitely many solutions.

Front

What is the first step to solve the equation 5x - 4 + 2x = 3?

Back

Combine like terms: 7x - 4 = 3.

Front

What is the solution to the equation 7x - 4 = 3?

Back

Add 4 to both sides: 7x = 7, then divide by 7: x = 1.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation, often occurring when the variable cancels out and results in a false statement.

Front

What is the solution to the equation 2x + 1 = 2x - 1?

Back

Subtract 2x from both sides: 1 = -1, which is a false statement, indicating no solution.