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Chapter 4: Problem 88

Solve. $$ q+31=72 $$

Short Answer

Expert verified
q = 41

Step by step solution

01

Understand the equation

The given equation is simple linear equation in the form of \( q + 31 = 72 \). The goal is to solve for the variable 'q'.
02

Isolate the variable

Subtract 31 from both sides of the equation to isolate the variable 'q'. This gives: \( q + 31 - 31 = 72 - 31 \).
03

Simplify

Simplify both sides of the equation. The left side becomes just 'q' since \( q + 31 - 31 \) cancels out the 31. The right side simplifies to 41. Hence, \( q = 41 \).

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Key Concepts

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

linear equations
Linear equations are fundamental in algebra and they appear frequently in various real-world scenarios.
They are equations where the highest power of the variable is 1.
In our example, the given linear equation is in the form of: q + 31 = 72.
This indicates that the variable 'q' is raised to the power of 1.
Linear equations typically have one solution.
The main goal in solving a linear equation is to find the value of the variable that makes the equation true.
For this, we need to use algebraic techniques to manipulate the equation.
isolate the variable
Isolating the variable is one of the key steps when solving linear equations.
It means making the variable stand alone on one side of the equation.
We do this by performing inverse operations to both sides of the equation.
Inverse operations are operations that undo each other.
  • For instance, if a number is added to the variable, we subtract the same number from both sides.
  • If a number is multiplied by the variable, we divide both sides by that number.
In our exercise, we have the equation: q + 31 = 72.
To isolate 'q', we need to get rid of the 31 that is added to 'q'.
We do this by subtracting 31 from both sides of the equation:
q + 31 - 31 = 72 - 31.
After performing this operation, we get: q = 41.
This leaves 'q' isolated, meaning we have successfully solved for 'q'.
simplification step
The simplification step involves reducing the equation to its simplest form so that the solution becomes clear.
After isolating the variable, we need to simplify any arithmetic that remains.
Consider the equation after subtracting 31 from both sides:
q + 31 - 31 = 72 - 31.
The terms 31 - 31 cancel each other out, leaving us with just 'q' on the left side.
The right side simplifies to 72 - 31, which equals 41.
Therefore, the simplified equation is:
q = 41.
This is our final solution, showing that 'q' equals 41.
It's always important to check your work by substituting the solution back into the original equation to verify it meets the equation's requirements.

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