91Ó°ÊÓ

When solving equations, one common task is isolating a specific variable. In the exercise provided, we needed to solve for the variable c. This process involves rearranging the equation so that c stands alone on one side. We start with the given equation, \(180 = a + b + c\). To isolate c, we subtract both a and b from both sides. Here's a quick breakdown:
• Start with the original equation: \(180 = a + b + c\).
• Subtract a: \(180 - a = b + c\).
• Then, subtract b: \(180 - a - b = c\).
In the end, we have c isolated: \(c = 180 - a - b\). This step-by-step rearrangement helps us clearly understand how to isolate the variable we are solving for.

Linear equations are a fundamental part of algebra. They are called linear because they graph as straight lines. In simpler terms, a linear equation is any equation that can be written in the form \(Ax + By = C\). In our example, the equation \(180 = a + b + c\) is a linear equation involving three variables: a, b, and c. Some key traits of linear equations include:
• They contain no exponents or powers on the variables;
• All variables are to the first power and appear only in their own terms;
• They can be solved using basic algebraic methods like addition, subtraction, multiplication, and division.
Understanding these key points about linear equations helps us recognize how to approach and solve them effectively.

Algebraic manipulation is a crucial skill for solving equations. It involves using mathematical operations to rearrange and simplify equations. In our exercise, we used algebraic manipulation to isolate the variable c. Here are the steps we followed:
• First, identify the variable to be isolated—in this case, c.
• Then, perform inverse operations to move other variables and constants to the other side of the equation. For instance, subtracting a and b from both sides.
• Finally, rearrange the equation to get the variable by itself: \(c = 180 - a - b\).
Besides isolating variables, algebraic manipulation includes other techniques like factoring, distributing, and combining like terms. These techniques help to simplify complex equations and make solutions clearer and more understandable.