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

How do you solve the equation x – 5 = 3 – x?

Back

Add x to both sides: 2x - 5 = 3. Then add 5 to both sides: 2x = 8. Finally, divide by 2: x = 4.

Front

What is the solution to the equation 2 – 5x = -7x?

Back

x = -1.

Front

How do you solve the equation 6x - 7 = 5x + 1?

Back

Subtract 5x from both sides: x - 7 = 1. Then add 7 to both sides: x = 8.

Front

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

Back

x = 3.

Front

How do you solve the equation 3(x + 9) = 6x?

Back

Distribute: 3x + 27 = 6x. Then subtract 3x from both sides: 27 = 3x. Finally, divide by 3: x = 9.

Front

What is the first step in solving an equation with variables on both sides?

Back

Identify and isolate the variable by moving all terms involving the variable to one side of the equation.

Front

What does it mean to isolate a variable in an equation?

Back

To manipulate the equation so that the variable is alone on one side, making it easy to find its value.

Front

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

Back

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

Front

What is a common mistake when solving equations with variables on both sides?

Back

Forgetting to perform the same operation on both sides of the equation.