Problem 43 - Basic College Mathematics

Question

Solve. $$ 3008=x+2134 $$

Step-by-Step Solution

Answer

x = 874

Step 1: Identify the equation

Understand the given equation: 3008 = x + 2134

Step 2: Isolate the variable

To find the value of x, we need to isolate it on one side of the equation. Subtract 2134 from both sides. 3008 - 2134 = x + 2134 - 2134

Step 3: Simplify the equation

Perform the subtraction on the left side to find the value of x. 3008 - 2134 = 874

Step 4: Write the final solution

After subtracting, we find that x = 874.

Key Concepts

Isolating Variables

Isolating variables is one of the foundational steps in solving linear equations. To solve for a variable means to get it by itself on one side of the equation. This allows you to see clearly what the variable equals. In the equation given: \[3008 = x + 2134\] we want to isolate \(x\). To do that, we need to remove 2134 from the right side.
We can do this by subtracting 2134 from both sides of the equation. This gives us: \[3008 - 2134 = x + 2134 - 2134\]
By performing the same operation on both sides, we're keeping the equation balanced. This step is crucial because it helps in maintaining the equality and correctly solving for the variable.

Basic Arithmetic

Understanding basic arithmetic operations like addition, subtraction, multiplication, and division is crucial when solving linear equations. In this particular problem, we used subtraction to isolate the variable: \[3008 - 2134\]
Here is a simple breakdown:

• Write down the equation: 3008 - 2134
• Subtract the units column: 8 - 4 = 4
• Subtract the tens column: 0 - 3 (here, we need to borrow 1 from the hundreds column making it 10 - 3 = 7)
• Subtract the hundreds column: 9 - 1 = 8
• Lastly, subtract the thousands column: 2 - 2 = 0 (since we borrowed 1 already, it was actually 3 - 2)

Hence, after the subtraction, we get 874. Basic arithmetic helps in simplifying and solving equations accurately.

Simplifying Equations

Once you isolate the variable, the next step is to simplify the equation to get the final answer. For the problem at hand, after isolating \(x\), we were left with: \[3008 - 2134\]
Simplifying means performing the arithmetic operation to get a single number. In this case: \[3008 - 2134 = 874\]
Thus, the equation simplifies to: \[x = 874\]
Simplifying also involves checking your work to ensure no errors in arithmetic operations. It's a valuable practice to verify each step to ensure that the solution is accurate. Remember, simplifying is not just about making the equation smaller but also about making it clearer and conclusive.