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Chapter 2: Problem 21

Solve each linear equation. Show your work and check your answer. $$-72-x=15$$

Short Answer

Expert verified
The solution is \(x = -87\).

Step by step solution

01

Isolate the variable term

First, add 72 to both sides of the equation to isolate the term with the variable.\[-72 - x + 72 = 15 + 72\]This simplifies to:\[-x = 87\]
02

Solve for the variable

Next, multiply both sides of the equation by -1 to solve for x.\[-1 \times (-x) = -1 \times 87\]This simplifies to:\[x = -87\]
03

Check your answer

Substitute x back into the original equation to verify your solution.\[-72 - (-87) = 15\]This simplifies to:\[-72 + 87 = 15\]Since 15 equals 15, the solution is verified.

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Key Concepts

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

Isolate the Variable
Isolating the variable is the first step in solving a linear equation. Our goal is to get the term with the variable alone on one side of the equation. In the given problem, \-72 - x = 15\, we begin by isolating the variable term, which is \-x\. To do this, we need to get rid of the constant term on the same side as the variable. We add 72 to both sides of the equation to cancel out the \-72\: \[ -72 - x + 72 = 15 + 72 \] Simplifying this, we get: \[ -x = 87 \] Now, the variable term \-x\ is isolated.
Solve for Variable
Once the variable term is isolated, the next step is to solve for the variable. Here, we have \-x = 87\ and we need to find the value of \x\. Since \-x\ means the variable \x\ is multiplied by \-1\, we do the opposite operation to solve for \x\. Multiplying both sides by \-1\ will remove the negative sign: \[ -1 \times (-x) = -1 \times 87 \] Which simplifies to: \[ x = -87 \] Now we have the value of \x\, which is \-87\.
Verify Solution
It's crucial to verify your solution to ensure that it's correct. To do this, substitute the value of the variable back into the original equation and see if both sides are equal. In our example, we substitute \x = -87\ back into \-72 - x = 15\: \[ -72 - (-87) = 15 \] Simplifying this, we get: \[ -72 + 87 = 15 \] Since \15 = 15\, our solution \x = -87\ is correct. Verification helps avoid mistakes and confirms that the solution satisfies the original equation.

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