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Chapter 2: Problem 13

Solve each equation, and check your solution. $$ x+28=19 $$

Short Answer

Expert verified
x = -9

Step by step solution

01

Isolate the variable

To solve for x, isolate the variable on one side of the equation. Subtract 28 from both sides.\[ x + 28 - 28 = 19 - 28 \]\[ x = -9 \]
02

Verify the solution

Substitute \( x = -9 \) back into the original equation to verify the solution is correct.\[ (-9) + 28 = 19 \]\[ 19 = 19 \]Since both sides of the equation are equal, the solution is verified.

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Key Concepts

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

isolating the variable
When solving linear equations, the main goal is to find the value of the unknown variable. In this case, our variable is **x** and the equation is **x + 28 = 19.** To isolate the variable means to get it alone on one side of the equation. Start by performing the same operation on both sides of the equation to maintain equality. Here, we subtract 28 from both sides to isolate **x**: \( x + 28 - 28 = 19 - 28 \). This simplifies to: \( x = -9 \). Now, **x** is isolated, and we have found that **x = -9.** This fundamental step in solving linear equations helps to clearly identify the value of the unknown variable by strategically removing other numbers and terms.
checking solutions
After isolating the variable and finding **x = -9,** we must check our solution to confirm its accuracy. This verification step ensures that the solving process was correct. Substitute **x = -9** back into the original equation: \[ (-9) + 28 = 19 \]. Simplify the left side of the equation: \( -9 + 28 = 19 \), Which indeed equals 19. Both sides of the equation are now equal: \( 19 = 19 \) This confirms that our solution is correct. Checking solutions is a vital step in problem-solving because it assures that the value obtained for the variable satisfies the given equation.
basic algebra
Understanding how to solve linear equations is part of basic algebra. It involves using simple operations like addition, subtraction, multiplication, and division. These operations help balance the equation to keep both sides equal. When solving the equation **x + 28 = 19,** we used subtraction, a basic algebraic operation, to keep the equation balanced. The whole process can be summed up in a few key points:
  • Identify the variable.
  • Isolate the variable using inverse operations (like subtracting 28).
  • Simplify the equation until the variable is alone.
  • Check the solution by plugging it back into the original equation.

Mastering these basic operations in algebra is essential, as they are foundational for more advanced math topics. It builds problem-solving skills and logical reasoning, which are valuable in everyday life as well as in more complex math problems.

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