Solving Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that has variables (like x or y) on both sides of the equal sign, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation -6y + 17 = 3y - 10?

Back

Combine like terms by adding 6y to both sides: 17 = 9y - 10.

Front

What is the solution to the equation 5x + 15 = 10x - 40?

Back

x = 11.

Front

What does it mean to combine like terms?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

What is the solution to the equation 12 - 5k = k + 6?

Back

k = 1.

Front

What is the purpose of checking your solution in an equation?

Back

To verify that the solution satisfies the original equation, ensuring it is correct.

Front

What is the solution to the equation 4k + 24 = 6k - 10?

Back

k = 17.

Front

What is the process of solving an equation with variables on both sides?

Back

1. Move all variable terms to one side. 2. Move constant terms to the other side. 3. Isolate the variable.

Front

What is the solution to the equation 13y - 18 = -5y + 36?

Back

y = 3.