Equations with variables on both sides

Front

What is an equation with variables on both sides?

Back

An equation where the variable appears on both sides of the equal sign, requiring manipulation to isolate the variable.

Front

What is the first step to solve the equation 5x + 8 = 2x - 7?

Back

Subtract 2x from both sides to get 3x + 8 = -7.

Front

If a variable disappears and the remaining equation is true, what does it imply?

Back

All numbers are solutions to that equation.

Front

If a variable disappears and the remaining equation is not true, what does it imply?

Back

There is no solution to that equation.

Front

What is the solution to the equation 5x = 2x?

Back

x = 0.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to both sides of the equation.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation.

Front

What is the result of subtracting x from both sides of 5x + 14 = x + 11?

Back

4x + 14 = 11.

Front

What is the principle of balancing equations?

Back

Whatever you do to one side of the equation, you must do to the other side to maintain equality.

Front

What is a true statement in the context of equations?

Back

A statement that holds true for all values of the variable involved.