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Chapter 3: Problem 44

A certain number subtracted from 32 is 15 . What is the number?

Short Answer

Expert verified
The number is 17.

Step by step solution

01

Understand the Problem

We need to find the unknown number, let's call it \( x \). The problem states that when this number is subtracted from 32, the result is 15.
02

Set up the Equation

According to the problem, \( 32 - x = 15 \). This is the equation that represents the situation described.
03

Rearrange the Equation

To isolate \( x \), subtract 15 from 32: \[ x = 32 - 15 \]
04

Solve the Equation

Calculate the value: \[ x = 32 - 15 = 17 \]
05

Verify the Solution

Check if subtracting 17 from 32 gives you 15: \[ 32 - 17 = 15 \] Since it is correct, our solution is validated.

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Key Concepts

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

Understanding Linear Equations
Linear equations are like balance scales, making both sides equal. They are called "linear" because they graph as straight lines on a coordinate plane. In our exercise, the equation is simple:
  • Set up as: \( 32 - x = 15 \).
  • The unknown, \( x \), represents the number we need to find.
  • The arrangement shows subtraction, where \( x \) is subtracted from 32.
Linear equations are a foundational part of algebra and are used to solve problems involving an unknown value. They help us get valuable insight into the relationships between numbers. Understanding them simplifies more complex problems in mathematics.
Solving Problems Using Equations
When faced with a problem like finding a specific number, using equations makes it manageable. Problem-solving in algebra often involves these steps:
  • Identify what you need to find: Here, the unknown number so the solution must make \( 32 - x = 15 \).
  • Translate the problem into an equation: This is our central part where we apply algebra (i.e., setting \( 32 - x = 15 \)).
  • Manipulate the equation: This involves arranging it so that the unknown is isolated on one side. Rearrange to find \( x \) by subtracting 15 from 32.
  • Verify: Always check your solution by substituting back into the original equation to see if both sides match.
These structured steps help tackle different algebraic problems, fostering confidence and competence in students.
Subtraction in Algebra
Subtraction is not just about taking numbers away, it's about understanding relationships in equations. Here's how subtraction works in our example:
  • The given equation is \( 32 - x = 15 \).
  • This states that subtracting \( x \) from 32 results in 15.
  • To solve, rearrange to find the unknown: \( x = 32 - 15 \).
Subtraction helps reveal the unknown when given an outcome. It also underscores how numbers relate to each other, a fundamental concept in algebra. Understanding this will aid students in tackling more advanced math topics with greater ease.

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