Solving Equations with Variables on Both Sides_SWD

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 are variables in an equation?

Back

Variables are symbols (often letters) that represent unknown values in mathematical expressions or equations.

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 the left and right sides of the equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform operations to get the variable on one side of the equation and the constants on the other side.

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, by combining like terms.

Front

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

Back

Combining like terms helps to simplify the equation, making it easier to solve.

Front

What does it mean to 'move' a term from one side of the equation to the other?

Back

Moving a term involves adding or subtracting it from both sides of the equation to maintain equality.

Front

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

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.

Front

What is the solution to the equation: −3(x − 1) + 8(x − 3) = 6x + 7 − 5x?

Back

The solution is x = 7.