Equations with Variables on Both Sides

Front

What is an equation with variables on both sides?

Back

An equation that contains variables on both the left and right sides, requiring manipulation to isolate the variable.

Front

What is the first step to solve the equation 5(2x + 4) = 40?

Back

Distribute the 5 on the left side: 10x + 20 = 40.

Front

How do you isolate the variable in the equation 7 + 9x = 6x - 2?

Back

Subtract 6x from both sides to get 3x + 7 = -2.

Front

What is the solution to the equation 6 - x = 12 + 2x?

Back

x = -2.

Front

What does it mean to combine like terms in an equation?

Back

It means to simplify the equation by adding or subtracting terms that have the same variable and exponent.

Front

What is the solution to the equation 8x = 4x + 12?

Back

x = 3.

Front

What is the process to solve the equation 3 - 7x = x - 5?

Back

Add 7x to both sides and then add 5 to both sides to isolate x.

Front

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

Back

To verify that the solution satisfies the original equation and is correct.

Front

What does it mean to 'isolate the variable' in an equation?

Back

To manipulate the equation so that the variable is alone on one side of the equation.

Front

What is the solution to the equation 5(2x + 4) = 40?

Back

x = 2.