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Chapter 11: Problem 16

Solve using the addition principle. $$ x+13=-13 $$

Short Answer

Expert verified
x = -26

Step by step solution

01

Identify the Addition Principle

The addition principle states that if the same amount is added to both sides of an equation, the equality is maintained. The principle allows isolating the variable.
02

Set Up the Equation

The given equation is: \[ x + 13 = -13 \]
03

Cancel Out the Constant Term

To isolate the variable x, subtract 13 from both sides of the equation:\[ x + 13 - 13 = -13 - 13 \]
04

Simplify Both Sides

Simplify both sides to find:\[ x = -26 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

solving equations
Solving equations is an essential skill in algebra. It involves finding the value of the variable that makes the equation true. Let's break down the process with the given exercise:
  • The equation is:
  • Our goal is to find the value of
    of the equation


The primary steps for solving equations typically include:

  • Identifying the equation to solve.
  • Applying a principle or rule to isolate the variable.
  • Simplifying both sides of the equation to find the solution.
, In our example, we use the addition principle to isolate the variable.
variable isolation
Variable isolation is about getting the variable alone on one side of the equation. Let鈥檚 see how it is done in our example. To isolate x, we need to remove the constant that is added to it.
  • The given equation is:
    deskgx
  • To isolate we subtract the same constant from both sides.


    i.e
    subtract 13 from both sides:听

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