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Chapter 3: Problem 5

Decide which operation you would use first to solve the equation. $$x+8=0$$

Short Answer

Expert verified
The operation to use first to solve the equation is subtraction. The solution to the equation is \(x = -8\).

Step by step solution

01

Identify the operation necessary to isolate x

The operation needed to isolate x is subtraction. Since we have \(x + 8 = 0\), subtract 8 from both sides of the equation to isolate x.
02

Subtract 8 from both sides

When we subtract 8 from both sides, the equation becomes \(x + 8 - 8 = 0 - 8\), which simplifies to \(x = -8\).

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Key Concepts

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

Isolate Variable
Solving linear equations often involves finding the value of a variable that makes the equation true. To do this, we typically aim to isolate the variable鈥攖his means getting the variable on one side of the equation, by itself. In the given problem, the variable is represented by x, and it's combined with the number 8 in the term 'x + 8'.

The goal is to manipulate this equation such that x stands alone without any additional terms or coefficients. By doing so, we'll discover the value of x that solves the equation. Isolating a variable is a fundamental skill in algebra and provides a clear path toward finding solutions to more complex equations.
Subtraction Method
The subtraction method is a straightforward technique used to solve equations, implementable when you need to eliminate a term to isolate a variable. As seen in this exercise, we start with the equation \(x + 8 = 0\). To isolate x, we subtract 8 from both sides of the equation. This is because adding and subtracting the same number on both sides keeps the equation balanced鈥攚hat you do to one side, you must do to the other.

Applying the Subtraction Method

When we subtract 8 from each side of \(x + 8 = 0\), we get \(x + 8 - 8 = 0 - 8\). This simplifies to \(x = -8\). Thus, we've used the subtraction method to successfully isolate x and solve the equation.
Equation Operations
Understanding equation operations is crucial when solving any mathematical problem involving equations. Operations such as addition, subtraction, multiplication, and division can all be applied to manipulate an equation, allowing us to isolate the variable.

The operations must be applied equally to both sides to maintain the balance of the equation鈥攁 cornerstone principle known as the 'balance method'. It's important to reverse the operation that is currently applied to the variable. For example, if a variable is being added to a number, as with x in \(x+8=0\), we must subtract that number from both sides to cancel out the addition.

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Most popular questions from this chapter

Match the statement with the property it represents. (a) Addition Property of Inequality (b) Subtraction Property of Inequality (c) Multiplication Property of Inequality (d) Division Property of Inequality \(2>-6\), so \(2(7)>-6(7)\).

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