Problem 45 - Fundamentals of Mathematics

Question

Calculator Exercises. $$a-44.0014=-21.1625$$

Step-by-Step Solution

Answer

\(a = 22.8389\)

Step 1: Understand the Equation

The equation given is \(a - 44.0014 = -21.1625\). Here, \(a\) is the variable that we need to find. The equation shows that if we subtract 44.0014 from \(a\), the result should be -21.1625.

Step 2: Isolate the Variable

To solve for \(a\), we need to isolate \(a\) on one side of the equation. This can be done by adding 44.0014 to both sides of the equation. This step cancels out the -44.0014 on the left side of the equation. So, the equation becomes:

Step 3: Perform the Calculation

Now, we perform the arithmetic operation on the right side of the equation:\[a = -21.1625 + 44.0014\]Calculate the sum of these two numbers to find \(a\).

Step 4: Compute the Result

Calculate the sum:\[a = -21.1625 + 44.0014 = 22.8389\]Thus, \(a = 22.8389\).

Key Concepts

Solving Equations

To solve an equation means to find the value of the variable that makes the equation true. This starts with understanding the given equation, which is crucial for finding the unknown.
In our example, the equation is set up as \(a - 44.0014 = -21.1625\). Your goal here is to find out what \(a\) must be. The equation tells us that when we subtract 44.0014 from \(a\), we should end up with -21.1625.
This forms the basis for solving the equation, where you're frequently tasked with 'undoing' the operation that has been done to the variable.

Isolating Variables

Isolating variables is like doing detective work where you want to "uncover" the variable \(a\) on one side of the equation by itself. In simple terms, what we're doing is setting \(a\) free from any numbers that are attached to it on one side of the equation.
For the equation \(a - 44.0014 = -21.1625\), \(a\) is currently grouped with a subtraction of 44.0014. To "unattach" it, we can add 44.0014 to both sides. This is because adding is the opposite of subtracting, and helps balance the equation.
When you add 44.0014 to both sides, it cancels out the negative 44.0014 on the left, leaving you with only \(a\) on that side. This leads you to the new equation: \(a = -21.1625 + 44.0014\), already halfway done in finding \(a\).

Arithmetic Operations

Arithmetic operations are what allow us to compute numbers and solve the equations. Here, you specifically engage in addition, which is common when isolating a variable that has been subtracted by a number.
In our exercise, we performed the arithmetic operation of adding from the expression \(-21.1625 + 44.0014\). When you calculate this, the numbers add up to 22.8389.

• Start by focusing on the positive and negative signs. -21.1625 is a negative number, while 44.0014 is positive.
• This means, to add, you find the difference between the two absolute values (which are 44.0014 - 21.1625), resulting in 22.8389.

This step of arithmetic shows how even simple addition can be used to solve for a variable, leading us to conclude that \(a = 22.8389\).