Solving Equations with Variables on Both Sides

Front

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

Back

Subtract x from both sides to isolate the variable: 2x - x = 3.

Front

How do you isolate the variable in the equation 7w + 5 = 3w - 15?

Back

Subtract 3w from both sides and then subtract 5 from both sides.

Front

What is the solution to 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 process to solve 7x = 3x + 24?

Back

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

Front

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

Back

It means that the variable appears on both sides of the equal sign, requiring manipulation to isolate the variable.

Front

What is the solution to the equation 2a - 9 = 5a?

Back

Add 9 to both sides and then subtract 5a from both sides to find a = -3.

Front

What is the importance of checking your solution after solving an equation?

Back

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

Front

What is a variable in an equation?

Back

A symbol, often a letter, that represents an unknown value.

Front

What does it mean to 'isolate the variable'?

Back

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

Front

What is the equation 3x + 4 = 10 asking you to find?

Back

The value of x that makes the equation true.