Question

Determine the appropriate algebra property for the following: if 3x = 12, then x = 4.

Answer 1

The Division Property of Equality is used to solve the equation 3x = 12, resulting in x = 4 by dividing both sides by 3.

Step-by-step explanation:

The appropriate algebra property for the statement 'if 3x = 12, then x = 4' is known as the Division Property of Equality. This property states that if you divide both sides of an equation by the same nonzero number, the two sides remain equal. To solve for x, we divide both sides of the equation by 3, which is the coefficient of x. Here's the step-by-step process:

1. Start with the equation 3x = 12.
2. Divide both sides by 3: (3x)/3 = 12/3.
3. Simplify both sides: x = 4.

By doing this, we can see that x equals 4 when 3 times x equals 12. This is a simple yet fundamental concept in algebraic rearrangement and solving linear equations.