Variables on Both Sides

Front

What is a variable in mathematics?

Back

A symbol used to represent an unknown value in an equation or expression.

Front

What does it mean to solve an equation with variables on both sides?

Back

It means to find the value of the variable that makes both sides of the equation equal.

Front

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

Back

Combine like terms on both sides of the equation.

Front

If you have the equation 3x + 5 = 2x + 10, how do you isolate x?

Back

Subtract 2x from both sides to get x + 5 = 10, then subtract 5 from both sides to find x = 5.

Front

What is the solution to the equation 4x - 2 = 2x + 10?

Back

x = 6.

Front

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

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What does it mean if an equation has no solution?

Back

It means there is no value for the variable that can make the equation true.

Front

What is an example of an equation with no solution?

Back

The equation 2x + 3 = 2x - 5 has no solution because it simplifies to 3 = -5.

Front

What is an example of an equation with infinitely many solutions?

Back

The equation 3x + 6 = 3(x + 2) has infinitely many solutions because both sides are equivalent.

Front

What is the importance of balancing an equation?

Back

Balancing an equation ensures that both sides remain equal when performing operations.