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Chapter 2: Problem 20

\(x-15.5=-5.1\)

Short Answer

Expert verified
x = 10.4

Step by step solution

01

Add 15.5 to both sides

Start by isolating the variable x. To do this, add 15.5 to both sides of the equation: \( x - 15.5 + 15.5 = -5.1 + 15.5 \)
02

Simplify the equation

Simplify both sides of the equation: \( x = 10.4 \)

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Key Concepts

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

isolating the variable
When solving linear equations, we often need to isolate the variable. The variable is typically represented by letters like _(x)_ or _(y)_ and it's the value we're trying to find.
Isolating the variable means getting the variable alone on one side of the equation. To do this, we perform operations like addition, subtraction, multiplication, or division on both sides.
In the exercise example, we had the equation: \( x - 15.5 = -5.1 \).
To isolate _(x)_, we added 15.5 to both sides, as shown below:
\[ x - 15.5 + 15.5 = -5.1 + 15.5 \]
Adding 15.5 to both sides cancels out the -15.5 on the left, leaving _(x)_ by itself. Now we have:
\[ x = 10.4 \].
simplifying equations
Simplifying equations helps in solving them faster and with less error. Once we perform an operation on both sides of the equation, we should simplify to make the equation easier to read.
During simplification, combine like terms and perform basic arithmetic. For example, after adding 15.5 to both sides of our equation, it looks like this:
\[ x = -5.1 + 15.5 \]
Next, perform the addition on the right side:
\[ -5.1 + 15.5 = 10.4 \]
Thus, the simplified form of the equation becomes:
\[ x = 10.4 \]
addition property of equality
The addition property of equality states that if you add the same amount to both sides of an equation, the equality is still true.
This property is useful when you need to move terms in an equation. For instance, in our given problem, we started with:
\( x - 15.5 = -5.1 \).
We wanted to get rid of the -15.5 on the left to isolate _(x)_.
The addition property of equality lets us add 15.5 to both sides, like so:
  • \( x - 15.5 + 15.5 = -5.1 + 15.5 \)
  • On the left side, -15.5 and +15.5 cancel each other out.
  • On the right side, -5.1 plus 15.5 simplifies to 10.4.
In conclusion, the addition property of equality helps maintain balance in an equation while solving it.

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