91Ó°ÊÓ

Equation solving is a fundamental concept in algebra, where we find the value of the variable that makes the equation true. In the given exercise, the task is to solve the linear equation \(-16 = k - 12\).
To solve an equation means to find out what number the variable represents. A linear equation like this one involves equalizing two expressions by working with only one variable. The main goal is to manipulate the equation to express the variable by itself on one side of the equation while keeping the equation in balance.

• Start by understanding each term in the equation. Here, \(-16\) is a constant, and \(k - 12\) is an expression with the variable \(k\).
• The objective is to find the value of \(k\) that makes the entire statement true.

Linear equations often require few steps to solve, as they consist of the variable, numbers, and basic arithmetic operations (addition, subtraction, multiplication, or division).

Isolation of a variable is the method used to get the variable by itself on one side of the equation, thereby "solving" the equation.
This technique consciously focuses on balancing the equation by performing the same operation on both sides. Let's consider the exercise \(-16 = k - 12\). To solve for \(k\), you need to remove the \(-12\) attached to it.

• Start with the equation: \(-16 = k - 12\).
• Add 12 to both sides to balance out the subtraction done to \(k\): \((-16) + 12 = k - 12 + 12\).
• This simplifies to \(-4 = k\).

By isolating \(k\), we now know that the value of \(k\) required to make the equation valid is \(-4\). Mastering isolation requires practice with additive and multiplicative properties to rearrange terms efficiently.

Checking your solution is a crucial step to ensure reliability and accuracy. Once you have solved the equation, it's always a good practice to verify if your obtained solution meets the original equation criteria. In our example, after determining that \(k = -4\), the next step is to substitute back into the original equation to test its validity.
Substitute \(k = -4\) into the equation \(-16 = k - 12\):

• Replace \(k\) with \(-4\) resulting in \(-16 = (-4) - 12\).
• Simplify to check: \(-16 = -16\).
• Since the statement holds true, the solution \(k = -4\) is confirmed to be correct.

This step uncovers any possible computational errors made during isolation and symbol manipulation. Hence, checking solidifies your problem-solving skills and establishes confidence in your solutions.