91Ó°ÊÓ

Equation solving is the process of finding the value of the variables that make the equation true. When dealing with linear equations, our primary goal is to find a specific value for the variable that satisfies the equation.
In the provided exercise, the goal is to solve for the variable \(w\) in the equation \(2w + 10 = 5w - 5\). To do this, we can use steps that simplify the equation.
Here are some general steps to solve an equation:

• Combine like terms.
• Get all variable terms on one side of the equation.
• Get all constant terms on the other side of the equation.
• Isolate the variable by performing the inverse operation.

Following these steps helps in systematically reducing the problem, making it easier to find the solution.

Isolating variables implies manipulating the equation so that one side contains only the variable we are solving for. This process involves moving all other terms to the opposite side.
In the equation \(2w + 10 = 5w - 5\):

• First, we move all the \(w\) terms to one side: subtract \(2w\) from both sides, leading to \(10 = 3w - 5\).
• Next, we move the constant term (-5) to the other side by adding 5 to both sides, giving us \(15 = 3w\).
• Finally, to isolate \(w\), we divide both sides by 3. This results in \(w = 5\).

Remember, whatever you do to one side of the equation, you must do to the other side as well. This maintains the balance of the equation and ensures that your solution is correct.

Linear algebra is a branch of mathematics that focuses on vectors, vector spaces, and linear equations. Solving linear equations like the one in this exercise is a fundamental aspect of linear algebra.
A linear equation is one where the variable is raised to the power of one. The general form of a linear equation in one variable is \(ax + b = cx + d\). By applying linear algebra principles, we can:

• Combine like terms to simplify the equation.
• Use addition, subtraction, multiplication, or division to re-arrange terms.
• Isolate the variable to find the solution.

The given equation, \(2w + 10 = 5w - 5\), fits this pattern. By following steps to isolate \(w\), we effectively apply the principles of linear algebra to solve it. Understanding these principles lays a strong foundation for tackling more complex problems in mathematics and related fields.