Solving 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 7x = 4x + 33?

Back

Subtract 4x from both sides to get 3x = 33, then divide by 3 to find x = 11.

Front

What is the first step to solve 2x = x + 3?

Back

Subtract x from both sides to simplify the equation to x = 3.

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

How do you solve the equation 7x = 3x + 24?

Back

Subtract 3x from both sides to get 4x = 24, then divide by 4 to find x = 6.

Front

What is the solution to the equation 30 + 6t = 11t?

Back

Subtract 6t from both sides to get 30 = 5t, then divide by 5 to find t = 6.

Front

How do you solve the equation 6z = 49 - z?

Back

Add z to both sides to get 7z = 49, then divide by 7 to find z = 7.

Front

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

Back

To verify that the value found for the variable satisfies the original equation.

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.

Front

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

Back

To simplify the equation by adding or subtracting terms that have the same variable and exponent.