Equations with Variables on Both Sides

Front

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

Back

It means that the equation contains variables (like x, y, etc.) on both the left and right sides, requiring manipulation to isolate the variable.

Front

How do you isolate a variable in an equation with variables on both sides?

Back

To isolate a variable, you can add or subtract terms from both sides of the equation to get all instances of the variable on one side and constant terms on the other.

Front

What is the first step in solving the equation 14p - 8 = 22 + 20p?

Back

The first step is to move all terms involving p to one side of the equation, which can be done by subtracting 20p from both sides.

Front

What is the solution to the equation 8x - 8 = -4x + 16?

Back

The solution is x = 2.

Front

What is the principle of balancing equations?

Back

The principle of balancing equations states that whatever you do to one side of the equation, you must do to the other side to maintain equality.

Front

How do you check if your solution to an equation is correct?

Back

You can check your solution by substituting it back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 10x + 9 = 4x - 9?

Back

The solution is x = -3.

Front

What does it mean to simplify an equation?

Back

Simplifying an equation means to combine like terms and reduce the equation to its simplest form.

Front

What is the solution to the equation 5y + 34 = -2(-7y + 1)?

Back

The solution is y = 4.

Front

What is the importance of moving constants to one side of the equation?

Back

Moving constants to one side helps in isolating the variable, making it easier to solve the equation.