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Chapter 3: Problem 44

Fill in the blank with the appropriate number. $$______ -15=0$$

Short Answer

Expert verified
15

Step by step solution

01

Understand the Equation

The given equation is a basic subtraction equation where you need to find the number that, when subtracted by 15, equals 0. Represent the unknown number as a variable, say 'x'. So, the equation can be written as: \[ x - 15 = 0 \]
02

Isolate the Variable

To isolate 'x', add 15 to both sides of the equation. This step will help to solve for 'x'. \[ x - 15 + 15 = 0 + 15 \]
03

Simplify the Equation

Simplify both sides to find the value of 'x'. On the left side, -15 and +15 cancel each other out leaving x. On the right side, 0 + 15 equals 15. \[ x = 15 \]

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Key Concepts

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

solving equations
Solving equations involves finding the value of a variable that makes the equation true. In math, equations are like puzzles we need to solve to figure out the hidden number. For our example, the problem gives us this basic subtraction equation:
  • ______ -15=0
We need to find the blank (or the mystery number) that, when 15 is subtracted from it, equals 0. Let's call this mystery number 'x'. So our equation looks like this:

  • \( x - 15 = 0 \)






Next, we need to figure out the value of 'x'. To do this, we will use a critical skill called isolating variables.
isolating variables
Isolating the variable means getting the variable, in this case, 'x', alone on one side of the equation. Think of it as clearing everything around 'x' so we can see its value clearly. In the equation:
  • \( x - 15 = 0 \)
We want 'x' to be by itself on the left side. To do this, we need to get rid of the -15 next to it. We can do this by adding 15 to both sides of the equation. Here's how it's done:
  • \( x - 15 + 15 = 0 + 15 \)
Adding 15 to both sides cancels out the -15 on the left side and helps us move one step closer to isolating 'x'.
simplification process
The simplification process is about making the equation easier to read and understand. It's like cleaning up our math work! Let's continue from our previous step:
  • \( x - 15 + 15 = 0 + 15 \)
Now, we simplify both sides. On the left side, the -15 and +15 cancel each other out, leaving only 'x'. On the right side, 0 + 15 equals 15. So, we are left with:
  • \( x = 15 \)
So the solution to the equation is 15. This means that when you substitute 15 for the blank in the original problem, the equation:
  • 15 - 15 = 0
holds true. When simplifying, always perform the same operation on both sides of the equation to keep it balanced. This ensures that the equation remains correct and helps us find the right value for the variable.

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