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Chapter 2: Problem 92

Solve for \(x .\) Assume \(a, c, m \neq 0\) $$ x-4+a=a $$

Short Answer

Expert verified
x = 4

Step by step solution

01

Isolate the variable

Begin by simplifying the equation. Subtract 'a' from both sides of the equation: \( x-4+a - a = a - a \) Simplifying this, we get: \( x-4 = 0 \)
02

Solve for x

Next, add 4 to both sides to isolate 'x': \( x-4 + 4 = 0 + 4 \) Simplifying this, we have: \( x = 4 \)

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Key Concepts

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

Variable Isolation
Isolating the variable is a key step when solving linear equations. This means we need to get our unknown variable, in this case, 'x', on one side of the equation with everything else on the other side. In the given problem, we start with the equation:
\( x - 4 + a = a \).

To isolate 'x', we perform the same operation on both sides of the equation. Here, we subtract 'a' from both sides:
\( x - 4 + a - a = a - a \).

This simplifies to:
\( x - 4 = 0 \).

By doing this, we are left with 'x' on one side of the equation, making it easier to solve in the next steps.
Simplifying Equations
The process of simplifying equations helps us reduce the equation to a form where we can easily solve for the unknown variable. After isolating 'x' in our equation from the first step:
\( x - 4 = 0 \).

Notice that 'x' is not completely isolated yet because it is still being subtracted by 4. To simplify further, we need to get rid of the '-4'. We can do this by adding 4 to both sides of the equation:
\( x - 4 + 4 = 0 + 4 \).

This simplifies everything nicely to:
\( x = 4 \).

Through these simplifying steps, we make the equation as straightforward as possible, turning it into a direct solution.
Step-by-Step Solutions
A step-by-step approach is crucial for solving linear equations. It helps not only to avoid mistakes but also to understand the process deeply. Let's break down the entire solution into clear steps.

Step 1: Simplify the equation
  • Start with the original equation:
    \( x - 4 + a = a \).
  • Subtract 'a' from both sides:
    \( x - 4 + a - a = a - a \).
    This simplifies to:
    \( x - 4 = 0 \).

Step 2: Isolate the variable
  • We need 'x' alone on one side. Add 4 to both sides:
    \( x - 4 + 4 = 0 + 4 \).
    This gives us:
    \( x = 4 \).

Following these steps ensures accuracy and promotes a clear understanding of the solution.

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Most popular questions from this chapter

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