EQUATION (Variable on both sides)

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What is a variable in an equation?

Back

A variable is a symbol, often represented by letters like x or w, that stands for an unknown value in an equation.

Front

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

Back

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

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation 7w + 5 = 3w - 15?

Back

The first step is to get all terms containing the variable on one side and constant terms on the other side.

Front

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

Back

It means that there are countless values for the variable that satisfy the equation, often occurring when both sides are equivalent.

Front

What is the solution to the equation 3x + 15 = 3(x + 5)?

Back

The solution is infinitely many solutions, as both sides simplify to the same expression.

Front

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

Back

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

Front

What is the solution to the equation 7x + 19 = -2x + 55?

Back

The solution is x = 4.