Solving Multi-Step Equations with Variables on Both Sides

Front

What is a multi-step equation?

Back

An equation that requires more than one step to solve, often involving combining like terms, distributing, and isolating the variable.

Front

What does it mean to have variables on both sides of an equation?

Back

It means that the variable appears on both the left and right sides of the equation, requiring manipulation to isolate the variable.

Front

How do you solve the equation 4(2a + 3) = −3(a − 1) + 31?

Back

First, distribute: 8a + 12 = -3a + 3 + 31. Then combine like terms and isolate 'a' to find a = 2.

Front

What is the first step in solving the equation 2a - 4(a - 5) = 10?

Back

Distribute -4 to a and -5: 2a - 4a + 20 = 10.

Front

What does it mean if an equation has infinite solutions?

Back

It means that any value for the variable will satisfy the equation, often resulting from identical expressions on both sides.

Front

What is the solution to the equation 3x + 2 = 3x + 2?

Back

Infinite Solutions or All Real Numbers.

Front

How do you determine if an equation has no solution?

Back

If simplifying the equation leads to a false statement, such as 0 = 5, it has no solution.

Front

What is the solution to the equation 12k + 15 = 35 + 2k?

Back

k = 2.

Front

What is the process of combining like terms?

Back

Adding or subtracting terms that have the same variable raised to the same power.

Front

What does it mean to isolate a variable?

Back

To manipulate the equation so that the variable is on one side by itself, making it easier to solve.