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Chapter 2: Problem 88

Solve each number word problem. The difference of a number and eight is four. Find the number.

Short Answer

Expert verified
The number is 12.

Step by step solution

01

Translate the problem into an equation

Identify the unknown number as the variable. Let the unknown number be represented by the variable . The problem states that the difference between this number and eight is four. This can be written as an equation: - 8 = 4.
02

Isolate the variable (Solve for n)

To find the value of , add 8 to both sides of the equation to isolate : - 8 + 8 = 4 + 8, which simplifies to = 12.
03

Verify the solution

Substitute the value of back into the original problem to verify: (12 - 8 = 4). Since both sides of the equation balance and the condition is satisfied, the solution is correct.

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Key Concepts

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

Number Word Problems
Number word problems can seem tricky at first, but they're just ways to describe mathematical equations using words.
Once you know how to translate words into numbers and operations, it gets easier.

Here's a friendly guide to help you with number word problems:
  • Identify the unknown number and assign it a variable name, usually we use n or x.
  • Read the problem carefully to understand what mathematical operations are described.
  • Translate the words into a math equation. For example, in the problem: 'The difference of a number and eight is four', the unknown number is n, the difference means subtraction, and the number eight becomes -8.
    The equation formed will be: n - 8 = 4.

Practice a few of these with different operations (addition, subtraction, multiplication, division) to get the hang of it.
Isolating Variables
Once you've translated the word problem into a linear equation, the next step is to solve for the unknown variable.
This process is called isolating the variable, and here's how you can do it in a friendly step-by-step manner:
  • Look at your equation: n - 8 = 4.
  • To isolate n, you need to get rid of the -8 on the left side. You do this by doing the opposite operation, which is addition in this case.
  • Add 8 to both sides of the equation to keep it balanced: n - 8 + 8 = 4 + 8.
  • This simplifies to n = 12.

By performing the same operation on both sides of the equation, we isolate the variable and find its value. Remember: the key is to perform the opposite operation to cancel out the constant term on the variable side.
Verifying Solutions
Verifying your solution is like proofreading your answer. It's a crucial step to make sure you've done everything correctly.
Here's how to do it:
  • Take the value of the variable you've found. In this case, we found n = 12.
  • Substitute this value back into the original equation to see if it satisfies the condition.
  • The original equation was: n - 8 = 4. So, substitute 12 in place of n: \( 12 - 8 = 4 \).
  • Simplify the left side: 4 = 4.
    This shows that our solution is correct because both sides of the equation are equal.

Always verify your answer, it's a reliable way to ensure accuracy. Happy solving!

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Most popular questions from this chapter

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Solve each inequality, graph the solution, and write the solution in interval notation. \(\frac{3}{4} x-5 \geq-2\) and \(-3(x+1) \geq 6\)

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Solve. $$ 4|x-1|+2=10 $$

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