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The distributive property is a fundamental principle in algebra that allows us to multiply a single term with multiple terms inside parentheses. It helps to simplify expressions and solve equations effectively. For the exercise given, we have the equation:
\[ 4(-1) + 3y = 8 \] The term '4' is distributed to both terms inside the parentheses, i.e., it multiplies with '-1'.

• The operation performed is \( 4 \times (-1) = -4 \).

This results in the simplified expression:
\[ -4 + 3y = 8 \]
Using the distributive property correctly ensures clarity as it breaks down complex expressions into simpler parts that are easier to handle and solve. Understanding this property assists in overcoming difficulties in more complicated algebraic operations. Practice this skill to enhance your problem-solving techniques.

Solving equations is the process of finding the value of the unknown variable that makes the equation true. It involves performing operations that simplify the equation until the variable is isolated. In our example, after applying the distributive property, we ended up with:
\[ -4 + 3y = 8 \]
The goal is to transform the equation into a simpler form. We achieve this by performing operations that eliminate numbers from one side:

• By adding 4 to both sides, we cancel out the \(-4\) and simplify:
• \[ -4 + 4 + 3y = 8 + 4 \]

This simplification results in:
\[ 3y = 12 \]
The process of solving equations involves a step-by-step approach where equal operations on both sides maintain the balance of the equation. This is a crucial skill that will help tackle various types of mathematical problems.

Isolating variables is a key technique in algebra, especially when solving equations. It allows you to find the direct value of the unknown variable. Once equations are simplified, the next step is to isolate the variable so you can solve for its value. In our exercise, after simplifying to:
\[ 3y = 12 \]
We isolate \( y \) by performing the operation of dividing both sides by 3:

• This makes the equation \( \frac{3y}{3} = \frac{12}{3} \).

This step simplifies to:
\[ y = 4 \]
By dividing both sides, we successfully isolate the variable \( y \), revealing its correct value. Mastering this skill is essential as it simplifies solving equations in algebra, making maths more manageable.