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 an equation with variables on both sides?

Back

To solve, you can first move all terms involving the variable to one side and constant terms to the other side, then simplify and isolate the variable.

Front

What is the formula for the perimeter of a rectangle?

Back

The perimeter P of a rectangle is given by the formula P = 2(length + width).

Front

What is the formula for the area of a rectangle?

Back

The area A of a rectangle is given by the formula A = length × width.

Front

If the perimeter and area of a rectangle are equal, what can be inferred about its dimensions?

Back

The dimensions of the rectangle must satisfy the equation 2(length + width) = length × width.

Front

What is the value of x in the equation 3x + 5 = 2x + 12?

Back

x = 7.

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 that there are no values for the variable that can satisfy the equation, often resulting in a contradiction.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that any value for the variable satisfies the equation, often resulting in an identity.

Front

What is the significance of isolating the variable in an equation?

Back

Isolating the variable allows you to find its value, which is the solution to the equation.