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Chapter 2: Problem 11

\(x-12=19\)

Short Answer

Expert verified
x = 31

Step by step solution

01

Understand the Equation

The given equation is linear and can be written in the form of a linear equation in the format of: \(x-12=19\)
02

Isolate the Variable

To solve for \(x\), add \(12\) to both sides of the equation to cancel out the \(-12\) on the left side: \(x-12+12 = 19+12\)
03

Simplify the Equation

Simplify both sides of the equation:\(x = 31\)

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Key Concepts

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

Isolate the Variable
To solve linear equations, we need to isolate the variable. Isolating the variable means to get the unknown variable, often represented as 'x', by itself on one side of the equation. This makes it easier for us to find its value. Let's consider the equation: \(x - 12 = 19\).
Our goal is to get 'x' by itself. To do this, we need to remove the \-12\ from the left side. We can do this by performing the same operation on both sides of the equation. In this case, we add \12\ to both sides:
\(x - 12 + 12 = 19 + 12\).
The \-12 + 12\ cancels out and we are left with:
\(x = 31\).
Simplify the Equation
Once you've isolated the variable, the next step is to simplify the equation if needed. In our example:
\(x - 12 + 12 = 19 + 12\).
When you add \12\ to both sides, you simplify the expression. The left side becomes \x\ because \-12 + 12\ equals zero. The right side becomes \31\ since \19 + 12\ equals 31. Thus, after simplifying both sides, we get:
\(x = 31\).
At this stage, the equation is as simple as it can be, clearly showing the value of our variable 'x'.
Additive Inverse
The concept of additive inverse is essential in solving linear equations. The additive inverse of a number is what you add to that number to get zero. For example, the additive inverse of -12 is +12 because:
\(-12 + 12 = 0\).
We use the additive inverse to eliminate terms and isolate the variable. In our equation:
\(x - 12 = 19\),
we added +12 to both sides since +12 is the additive inverse of -12. This cancellation helps isolate our variable while maintaining equality on both sides:
\(x - 12 + 12 = 19 + 12\).
The left side simplifies to 'x' and the right side simplifies to 31, giving us the final result:
\(x = 31\).

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Most popular questions from this chapter

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