Problem 42 - Prealgebra

Question

Find the value of \(180-x\) when \(x=25\).

Step-by-Step Solution

Answer

The value of \(180-x\) when \(x=25\) is 155.

Step 1: Understanding the Expression

The expression given is \(180 - x\). We need to find the value of this expression when \(x = 25\).

Step 2: Substitute the Value of x

Replace \(x\) in the expression with 25. This gives us \(180 - 25\).

Step 3: Perform the Subtraction

Subtract 25 from 180. The calculation is: \[180 - 25 = 155\]

Step 4: Verify the Calculation

Check the subtraction by adding the result to the subtracted number to see if it returns the original number before subtraction.\[155 + 25 = 180\]. This confirms that our subtraction was accurate.

Key Concepts

Subtraction

Subtraction is one of the basic arithmetic operations and is essentially about finding the difference between two numbers. In the expression \(180 - x\), subtraction is used to determine how much smaller a number \(x\) is compared to 180. This operation is represented by the minus sign \(-\). When performing subtraction:

• Start from the leftmost digit and move right.
• If the digit being subtracted is larger than the digit it is subtracted from, borrowing from the next left digit is necessary.
• Carry out the subtraction for each digit systematically.

For our example, subtracting 25 from 180 is straightforward, mainly because 180 and 25 can be aligned easily; simply subtract 25 from 180 to get 155.

Variable Substitution

Variable substitution is a useful technique where a known value replaces a variable within an expression or equation. It simplifies the equation, allowing us to solve it efficiently. In the given exercise, the expression is \(180 - x\) with \(x = 25\).To apply substitution:

• Identify the variable to be substituted, \(x\) in this case.
• Replace every instance of \(x\) in the equation or expression with the value provided, which is 25.
• This transforms the expression from \(180 - x\) to \(180 - 25\).

Substitution offers clarity, making it easier to carry out subsequent arithmetic operations, such as subtraction, as demonstrated in our calculation.

Verification of Results

Verification of results is a crucial step in any mathematical calculation to ensure the accuracy of the solution. After performing an arithmetic operation, checking the result helps confirm that the work done is correct.In arithmetic subtraction, this can be done by performing an inverse operation. For our exercise, after finding that \(180 - 25 = 155\), we verify by adding the result, 155, back to the subtracted number, 25.If the sum, \(155 + 25\), equals the original number, 180, then the subtraction was performed correctly. This simple technique is invaluable in double-checking your calculations, providing assurance that the conclusion reached is accurate.