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Chapter 1: Problem 8

Solve. \(4-x=-5\)

Short Answer

Expert verified
x = 9

Step by step solution

01

Identify the equation

Recognize the given equation: `4 - x = -5`.
02

Isolate the variable

To isolate the variable `x`, subtract 4 from both sides of the equation: `4 - x - 4 = -5 - 4`.
03

Simplify the equation

Simplify both sides to get: `- x = -9`.
04

Solve for the variable

To solve for `x`, multiply both sides by -1 to get: `x = 9`.

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Key Concepts

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

Linear Equations
Linear equations are a type of equation that involves variables to the first power. They usually look like this: \(ax + b = c\). Linear equations form a straight line when graphed. They are the foundation for many areas of algebra. Understanding them well is crucial for solving more complex math problems.
  • They involve constants (numbers that don't change) and variables (symbols that represent numbers).
  • The goal is to find the value of the variable that makes the equation true.
  • They can have one variable, like in \(4 - x = -5\), or more.
Isolation of Variable
Isolating the variable means getting the variable on one side of the equation by itself. This helps us find the value of the variable.
  • We use inverse operations. For example, if a number is added to the variable, we subtract that number from both sides.
  • In the exercise, we subtracted 4 from both sides to isolate \(-x\):
  • \(4 - x - 4 = -5 - 4\)

After simplifying, we got \(-x = -9\). Our goal is to make sure \(x\) is alone on one side of the equation.
Simplification Steps
Simplification is breaking down the equation into simpler terms until we solve for the variable. Let's break it down:
  • After isolating the variable, we had \(-x = -9\).
  • To solve for \(x\), we multiply both sides by -1. This is because \(-x\) actually means \(-1 \times x\):
  • \((-1) \times (-x) = (-1) \times (-9)\)
  • This simplifies to \(x = 9\), which means we've found the value of \(x\).

By following these steps, we've solved the original equation. The variable \(x\) has been isolated, and we've simplified our way to the solution!

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