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 rearranging 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, if possible, and then move all terms involving the variable to one side and constant terms to the other side.

Front

How do you combine like terms in an equation?

Back

You add or subtract coefficients of the same variable or constant terms to simplify the equation.

Front

What is the importance of maintaining equality when solving equations?

Back

Maintaining equality ensures that any operation performed on one side of the equation must also be performed on the other side to keep the equation balanced.

Front

What is the solution to the equation -6n - (23/7)n = (93/7) + 4n?

Back

The solution is n = -1.

Front

How do you distribute a number across parentheses in an equation?

Back

You multiply the number by each term inside the parentheses.

Front

What is the solution to the equation -8(2a - 2) = -40 - 8a?

Back

The solution is a = 7.

Front

What does it mean to isolate the variable in an equation?

Back

Isolating the variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the solution to the equation 5 + 7(5m + 8) = -2m + 24?

Back

The solution is m = -1.

Front

What is the solution to the equation 6(x + 2) + 8(x + 2) = -6x - 8x?

Back

The solution is x = -1.