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Chapter 2: Problem 52

Translate to an equation and then solve it. The sum of \(x\) and -15 is 23 .

Short Answer

Expert verified
x = 38.

Step by step solution

01

Identify the relationship

The problem states that the sum of a number, which we will call \( x \), and -15 is 23. This can be written as an equation.
02

Set up the equation

Translate the words into a mathematical equation: \( x + (-15) = 23 \).
03

Simplify the equation

Combine the terms to make it easier to solve: \( x - 15 = 23 \).
04

Solve for \( x \)

Add 15 to both sides of the equation to isolate \( x \): \( x - 15 + 15 = 23 + 15 \). This simplifies to: \( x = 38 \).

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Key Concepts

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

Translating Word Problems into Equations
Understanding how to translate word problems into equations is a crucial skill in math. To tackle the given problem, we first need to identify key information from the text. For example, if the problem says 'The sum of a number and -15 is 23,' we can break this down:
  • 'The sum' indicates addition.
  • 'A number' is the unknown value we are solving for and can be represented by a variable like \( x \).
  • '-15' is a given number involved in the addition.
  • 'Is' signifies equality, indicating that the expression equals the number on the other side.
  • '23' is the total we get from the sum.
By identifying these elements, we can create the equation \( x + (-15) = 23 \). This allows us to move from a word problem to a solvable mathematical equation.
Simplifying Equations
Simplifying equations can make them easier to solve. In our problem, we started with the equation \( x + (-15) = 23 \). To put this into a simpler form, we can combine like terms.
Since adding a negative number is the same as subtracting that number, \( x + (-15) \) simplifies to \( x - 15 \). This makes our equation \( x - 15 = 23 \).
Simplifying equations by combining like terms or reducing the number of operations needed helps us see the path to the solution more clearly.
Isolating Variables
Once we have a simplified equation, our next goal is to isolate the variable. Isolating the variable means getting \( x \) alone on one side of the equation so we can find its value. For \( x - 15 = 23 \), we need to get rid of the -15 that is with \( x \).
We do this by performing the opposite operation. Here, subtracting 15 from \( x \) can be undone by adding 15. So, we add 15 to both sides of the equation: \[ x - 15 + 15 = 23 + 15 \] This simplifies to \[ x = 38 \]
By isolating the variable, we've found that \( x = 38 \). This step is crucial in solving any linear equation.

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