Solving Equations with Variables on Both Sides

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 the manipulation of the equation to isolate the variable.

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, which may include combining like terms.

Front

How do you combine like terms in an equation?

Back

You combine like terms by adding or subtracting coefficients of the same variable.

Front

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

Back

Isolating the variable allows you to find its value by getting it alone on one side of the equation.

Front

What is the significance of the equality sign in an equation?

Back

The equality sign indicates that the expressions on both sides of the equation are equal in value.

Front

How do you move a term from one side of the equation to the other?

Back

You move a term by performing the opposite operation; for example, if you have +5 on one side, you subtract 5 from both sides.

Front

What does it mean to check your solution after solving an equation?

Back

Checking your solution means substituting the found value back into the original equation to verify that both sides are equal.

Front

What is the result of the equation −7x − 3x + 2 = −8x − 8?

Back

The solution is x = 5.

Front

What is the result of the equation −14 + 6b + 7 − 2b = 1 + 5b?

Back

The solution is b = -8.

Front

What is the result of the equation −10 + x + 4 − 5 = 7x − 5?

Back

The solution is x = -1.