Solve Equations with Variables 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 with variables on both sides?

Back

It means to find the value of the variable that makes both sides of the equation equal, often requiring rearranging the equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

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

Back

The first step is to simplify both sides of the equation if necessary, and then move all variable terms to one side.

Front

What is the purpose of combining like terms in an equation?

Back

Combining like terms simplifies the equation, making it easier to solve for the variable.

Front

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

Back

Subtract 2x from both sides to get x + 5 = 10.

Front

What do you do after moving all variable terms to one side?

Back

After moving the variable terms, isolate the variable by performing inverse operations on the constant terms.

Front

In the equation 4x - 3 = 2x + 5, what is the value of x?

Back

x = 4.

Front

What is the significance of checking your solution in an equation?

Back

Checking your solution ensures that the value you found satisfies the original equation.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there is no value for the variable that makes both sides equal.