Equations with Variables on Both Sides (no fractions)

Front

What is the first step to solve an equation with variables on both sides?

Back

The first step is to isolate the variable on one side of the equation by moving all terms containing the variable to one side and constant terms to the other side.

Front

How do you combine like terms in an equation?

Back

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

Front

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

Back

Isolating a variable means rearranging the equation so that the variable is alone on one side, making it easier to solve for its value.

Front

What is the solution to the equation 7w + 5 = 3w - 15?

Back

The solution is w = -5.

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 process to solve the equation 14p - 8 = 22 + 20p?

Back

First, move all terms involving p to one side and constant terms to the other side, then combine like terms and solve for p.

Front

What is the solution to the equation 5x - 14 = 8x + 4?

Back

The solution is x = -6.

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when the variable cancels out and results in a false statement, such as 0 = 5.

Front

What is the solution to the equation 2c - 12 = 9c + 2?

Back

The solution is c = -2.

Front

How do you handle negative coefficients when solving equations?

Back

You treat negative coefficients like any other number; you can add, subtract, multiply, or divide as needed to isolate the variable.