Solving Equations with Variables on Both Sides

Front

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

Back

The first step is to isolate the variable terms on one side of the equation by adding or subtracting terms from both sides.

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 does it mean to isolate a variable in an equation?

Back

Isolating a variable means to manipulate the equation so that the variable is alone on one side of the equation.

Front

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

Back

x = -6.

Front

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

Back

You substitute the solution back into the original equation to see if both sides are equal.

Front

What is the principle of equality in solving equations?

Back

The principle of equality states that if you perform the same operation on both sides of an equation, the two sides remain equal.

Front

What is the solution to the equation 14p - 8 = 22 + 20p?

Back

p = -5.

Front

What is the distributive property and how is it used in solving equations?

Back

The distributive property states that a(b + c) = ab + ac. It is used to eliminate parentheses in equations.

Front

What is the solution to the equation 12x - 15 = 3(2x + 3)?

Back

x = 4.

Front

How do you handle negative coefficients when solving equations?

Back

You can multiply or divide both sides of the equation by a negative number, remembering to reverse the inequality if applicable.