/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 141 Solve each equation. $$-x=-8$$... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 141

Solve each equation. $$-x=-8$$

Short Answer

Expert verified
The solution is \(x = 8\).

Step by step solution

01

Isolate the Variable

The goal is to solve for the variable \(x\). In the equation \(-x = -8\), the variable \(x\) is already isolated but with a negative sign. To isolate \(x\) without the negative, multiply both sides of the equation by \(-1\).
02

Multiply Both Sides by -1

When we multiply both sides of the equation by \(-1\), we get: \(-1 \times (-x) = -1 \times (-8)\). This simplifies to: \(x = 8\).
03

Verify the Solution

To ensure the solution is correct, substitute \(x = 8\) back into the original equation: \(-x = -8\). Substituting \(x\) gives \(-8 = -8\), which is a true statement.

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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, the primary goal is to find the value of the variable that makes the equation true. The variable in your equation is the unknown part, commonly represented by letters such as \(x\). To isolate the variable means to get it by itself on one side of the equation.

Let's consider the given equation: \(-x = -8\). Here, the variable \(x\) is already alone, but it has a negative sign attached to it. This negative sign is technically making \(x\) 'not fully isolated'. So, to fully isolate \(x\), we should remove the negative sign. This brings us to our next step...
Multiply Both Sides of the Equation
To eliminate the negative sign and isolate \(x\), you'll need to multiply both sides of the equation by \(-1\). This method keeps the equation balanced. Imagine a balanced scale; if you add or remove something from one side, you must do the same to the other to keep it balanced.

In our case, multiply both sides of the equation \(-x = -8\) by \(-1\):
\( -1 \times (-x) = -1 \times (-8) \).

This can be simplified to: \( x = 8 \). Now, we have successfully isolated \(x\) without any negative signs, making the equation easier to understand and solve.
Verify the Solution
Once we have a solution, it鈥檚 essential to verify it to ensure accuracy. Verification involves substituting the found value back into the original equation. This step checks if your calculated value makes the original equation true.

Substituting \( x = 8 \) into the original equation \( -x = -8 \) gives:
\( -8 = -8 \). Since both sides of the equation are equal, our solution \( x = 8 \) is verified. This true statement confirms our calculation and verifies that our steps to isolate the variable and solve the equation were accurate.

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