/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 \(x+21.5=-13.4\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 22

\(x+21.5=-13.4\)

Short Answer

Expert verified
x = -34.9

Step by step solution

01

- Identify the equation

Recognize that the given equation is a linear equation: x + 21.5 = -13.4
02

- Isolate the variable

To isolate the variable x, subtract 21.5 from both sides of the equation: x + 21.5 - 21.5 = -13.4 - 21.5
03

- Simplify the equation

Simplify both sides of the equation: x = -34.9

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Key Concepts

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

headline of the respective core concept
A linear equation is a mathematical statement that shows the equality of two expressions with one unknown variable. These equations are called 'linear' because they graph as a straight line. The standard form of a linear equation is usually expressed as: ax + b = cHere, 'a' and 'b' are constants, and 'x' is the variable. Linear equations make foundational concepts in algebra clear and are extremely useful in real-life situations, such as calculating distances, budgeting money, or predicting trends in data.

In this specific exercise, the linear equation is: x + 21.5 = -13.4. Our task is to find the value of 'x' that makes this equation true.
headline of the respective core concept
Once we recognize the linear equation, the next step is to isolate the variable. 'Isolating the variable' means getting the variable by itself on one side of the equation to solve for it. Here's a step-by-step process:
  • Look at the equation and identify the variable you need to isolate, which in this case is 'x'.
  • To keep the equation balanced, perform the same mathematical operation on both sides of the equation.
  • In our example, we have 'x + 21.5 = -13.4'. To isolate 'x', we need to remove 21.5 from the left side. This can be done by subtracting 21.5 from both sides of the equation.
This action gives us: x + 21.5 - 21.5 = -13.4 - 21.5
This simplifies to: x = -34.9
Now, 'x' is isolated, and we have found its value.
headline of the respective core concept
Simplifying equations is a crucial step in solving linear equations. Simplifying makes equations more manageable and easier to solve. Here鈥檚 how to do it in our specific exercise:
  • First, after performing the operation to isolate the variable, carefully perform the arithmetic calculations.
  • Combine like terms where you add or subtract numbers directly based on their signs.
  • For our example, once we subtracted 21.5 from both sides of the equation, we simplified -13.4 - 21.5.
  • Carry out the simple arithmetic: -13.4 - 21.5, which gives -34.9.
Thus, the simplified equation is: x = -34.9
By adhering strictly to these processes鈥攔ecognizing the linear equation, isolating the variable, and simplifying the equation鈥攜ou can solve any linear equation correctly.

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