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Chapter 1: Problem 120

Determine whether 12 is a solution of \(35-a=13\)

Short Answer

Expert verified
12 is not a solution to the equation.

Step by step solution

01

- Understand the problem

We need to determine if 12 is a solution to the equation \(35 - a = 13\). To do this, we will substitute 12 for \(a\) and check if the equation holds true.
02

- Substitute 12 for a

Replace \(a\) with 12 in the equation: \(35 - 12 = 13\).
03

- Perform the subtraction

Calculate \(35 - 12\) to see if it equals 13. \[35 - 12 = 23\]
04

- Compare the result

Check if the result from Step 3 equals 13. Since 23 does not equal 13, the equation \(35 - 12 = 13\) is false.
05

- Conclusion

Since substituting 12 for \(a\) makes the equation false, 12 is not a solution to the equation \(35 - a = 13\).

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Key Concepts

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

Substitution Method
To determine whether a number is a solution to an equation, we can use the substitution method. This means we replace the variable in the equation with the number in question and see if the resulting expression is true. For example, with the equation \(35 - a = 13\)\, we substitute \(a\) with 12 and evaluate the left-hand side.
\(35 - 12\) results in 23, which is not equal to 13.
This verifies that 12 is not a solution. Substitution is a straightforward but powerful method for checking potential solutions.
It helps in understanding how different values affect the equation.
By substituting, you can quickly determine whether a value satisfies the conditions set by the equation.
Verification of Solutions
Verification is the process of checking whether a substituted value satisfies the original equation.
After substituting the target value, you perform the necessary arithmetic operations. In the example \(35 - a = 13\)\, we substituted 12 for \(a\) and calculated \(35 - 12 = 23\).
Since 23 does not equal 13, we confirmed that 12 is not a solution.
Verification is crucial to ensure your calculations are correct and that you've understood the problem. It involves detailed checks at every step to validate your results.
It is a final step that guarantees your solution is accurate.
Basic Algebra
Understanding basic algebra is essential for solving equations.
It involves manipulating symbols and numbers to find unknown values. In this example, we dealt with a simple linear equation \(35 - a = 13\)\.
Algebraic steps we used include:
  • Substituting a given number into the equation
  • Performing arithmetic operations
  • Comparing the outcome with the expected result
Basic algebra teaches you how to isolate variables and solve for unknowns by performing operations such as addition, subtraction, multiplication, and division.
Having a strong grasp of these fundamentals allows you to tackle more complex mathematical problems with confidence.

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