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In prealgebra, solving an equation typically involves finding the value of a variable that makes the equation true. An equation represents a balance between two expressions, usually separated by an equals sign \( = \). To solve the equation, your aim is to manipulate it until you isolate the variable on one side.
This process often requires a sequence of different operations, such as addition, subtraction, multiplication, or division, until you find the solution. Remember to always perform the same operation on both sides of the equation. This maintains the balance and keeps the equation valid under equality.

The distributive property is a fundamental principle that allows you to multiply a single term across terms inside parentheses. It states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products.
For example, suppose you have an expression like \( a(b+c) \). By applying the distributive property, you get:

• \( a \times b + a \times c \)

In the context of our example, you need to distribute \( 2 \) into \( (y + 12) \), which results in \( 2y + 24 \). Bringing terms out of the parentheses simplifies the current equation and makes the next steps forward clearer.

Variable isolation is crucial to finding a solution in any equation involving an unknown. The aim is to get the variable by itself on one side of the equation, typically the left side, which allows you to determine its value easily.
In the given exercise, after applying the distributive property, you have the equation \( 3y = 2y + 24 \). To isolate \( y \), subtract \( 2y \) from both sides, resulting in \( y = 24 \). By performing this operation, you've successfully isolated \( y \), solving the equation. Always check to make sure that any operations are balanced on each side to maintain equality. This process helps reinforce the concept of keeping equations balanced while solving.