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Chapter 11: Problem 7

Solve. What number added to 85 is \(117 ?\)

Short Answer

Expert verified
The number is 32.

Step by step solution

01

Understand the Problem

The problem asks what number, when added to 85, results in 117. In algebraic terms, it asks to solve for the unknown number.
02

Set Up the Equation

Represent the unknown number as a variable, say x. The problem can then be written as an equation: 85 + x = 117
03

Isolate the Variable

To solve for x, isolate the variable on one side of the equation. Subtract 85 from both sides of the equation: 85 + x - 85 = 117 - 85 x = 32
04

Verify the Solution

Verify the solution by substituting 32 back into the original equation: 85 + 32 = 117 Since both sides of the equation are equal, the solution is correct.

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Key Concepts

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

solving equations
Solving equations is a fundamental topic in algebra. The goal is to find the value of the unknown variable that makes the equation true. In our example, the equation is 85 + x = 117. Here, 'x' is the unknown number we need to find. Think of it like a puzzle where you have to figure out the missing piece. Always remember that whatever operation you do to one side of the equation, you must do the same to the other side to maintain balance.
addition
Addition is one of the basic arithmetic operations. In this problem, it involves combining numbers to get a sum. To grasp this better, consider simple instances like 2 + 3 = 5. Here, the question is 'What number can we add to 85 to get 117?' To set up the equation correctly, you should understand how addition works. Only by knowing these basics can you solve more complex problems involving variables and unknowns.
isolation of variables
Isolation of variables means getting the unknown variable on one side of the equation. This is crucial because it helps you solve for that variable. In our equation 85 + x = 117, we need to isolate 'x'. We can do this by subtracting 85 from both sides of the equation. Here's how it looks:
85 + x - 85 = 117 - 85
This simplifies to x = 32.
By isolating 'x', we brought the unknown down to a simple number, making it easier to solve the equation.
verification
Verification ensures that the solution we found is correct. It involves substituting the found value back into the original equation to check if it holds true. From our equation, we found x = 32. To verify:
85 + 32 = 117.
Since both sides of the equation are equal, we can be confident that x = 32 is indeed the correct solution. Verification is a crucial step in solving equations as it helps confirm your work and avoid mistakes.

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