Problem 53 Solve. $$ 13,083.3=x+12,500.... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 4: Problem 53

Solve. $$ 13,083.3=x+12,500.33 $$

Short Answer

Expert verified

x = 582.97

Step by step solution

Isolate the variable x

The goal is to solve for the variable x. To do this, isolate x on one side of the equation. Start by subtracting 12,500.33 from both sides of the equation.

Perform the subtraction

Subtract 12,500.33 from both sides: y = 13,083.3 - 12,500.33

Solve for x

Perform the subtraction to find the value of x: x = 13,083.3 - 12,500.33 = 582.97

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Key Concepts

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

Isolate the Variable

When solving linear equations, our main goal is to isolate the variable we're solving for, which is typically represented by 'x'. This means we want to have 'x' on one side of the equation by itself. This clear separation helps us understand what 'x' equals. For example, in the equation: \[13,083.3 = x + 12,500.33\], we need to perform certain operations to remove the other numbers or terms around 'x'. We often achieve this by using arithmetic operations such as addition or subtraction. Once 'x' is isolated, we can easily determine its value. This process is fundamental in algebra and helps in understanding more complex mathematical concepts.

Subtraction in Equations

Subtraction is a critical operation when solving equations. To isolate our variable, we often need to subtract numbers from both sides. This keeps the equation balanced, which is fundamental in algebra. For our example \[13,083.3 = x + 12,500.33\], we will subtract 12,500.33 from both sides. Doing so helps remove the 12,500.33 from the right side, simplifying our equation. Thus, our equation becomes: \[13,083.3 - 12,500.33 = x\]. This subtraction step is essential and must be performed carefully to ensure accuracy in our solution. Such operations are not just used in isolating variables but also in many other mathematical procedures.

Solving for x

Finally, after isolating the variable and performing necessary subtractions, we 'solve for x', which means we find the value of 'x'. In our equation, after isolating 'x' and performing the subtraction: \[13,083.3 - 12,500.33\], we get: \[x = 582.97\]. At this stage, we simply calculate the right side's value to find 'x'. This last step involves basic arithmetic, but it's crucial because it gives us the solution. Thus, 'solving for x' gives us the final numerical value of the variable we isolated. The accuracy of this step depends on all prior steps. Understanding the overall process ensures you can solve many similar equations confidently.

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91影视

Solve. $$ 13,083.3=x+12,500.33 $$

Short Answer

Step by step solution

Isolate the variable x

Perform the subtraction

Solve for x

Key Concepts

Isolate the Variable

Subtraction in Equations

Solving for x

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