Question

Write an equation that utilizes properties to find a solution.

Option a: y + 3(y - 2) = 4y - 6
Option b: 2x + (3 + 4) = 2x + 3 + 4
Option c: 5(2x - 1) = 10x - 5
Option d: 4a + 2b = 2(2a + b)

Answer 1

The question pertains to Mathematics, specifically in writing an equation using properties to find a solution. The best choice is option a, an identity equation, which exemplifies the application of the distributive property to solve for the variable 'y' with any real number being a solution.

Step-by-step explanation:

The subject is Mathematics and the problem asks to write an equation that uses properties to find a solution. The correct equation to use in this context is option a: y + 3(y - 2) = 4y - 6, as it shows how to utilize distributive property to solve for a variable.

To solve this equation, we distribute the '3' to both terms within the parentheses:

Step 1: y + 3(y - 2) = 4y - 6

Step 2: y + 3y - 6 = 4y - 6

Next, combine like terms on the left side:

Step 3: 4y - 6 = 4y - 6

As we can see, the equation simplifies to 0 = 0, which indicates that y can be any real number. This is an example of an identity equation, where both sides are always equal regardless of the value of y. Thus, it demonstrates the application of properties, such as distributive property, to find a solution to an equation.