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Chapter 1: Problem 23

Solve the given equation for \(\mathrm{x}\). $$ 5 x=5 $$

Short Answer

Expert verified
The solution is \(x = 1\).

Step by step solution

01

Identify the Equation

The equation given is \(5x = 5\). Our goal is to solve this equation for \(x\).
02

Isolate the Variable

To isolate \(x\), we need to divide both sides of the equation by 5, which is the coefficient of \(x\). This gives us \(x = \frac{5}{5}\).
03

Simplify the Equation

Simplify \(x = \frac{5}{5}\) to get \(x = 1\). By dividing 5 by 5, we find that \(x = 1\).

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Key Concepts

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

Solving Equations
Solving an equation is all about finding the value of the unknown variable that makes the equation true. When faced with an equation like \(5x = 5\), our job is to determine what value of \(x\) satisfies this equation. We approach this by manipulating the equation until \(x\) is by itself on one side. This process involves a sequence of steps that, when followed, help identify the solution. In this context, solving the equation entails applying mathematical operations that simplify our expressions and help us to isolate and eventually determine the value of the variable.
Isolating Variables
When we talk about isolating variables, we're referring to the process of getting the unknown variable by itself on one side of the equation. It involves using inverse operations to "undo" whatever has been done to the variable. Here's how it works:
  • Identify the operation connected to the variable that we need to reverse; in \(5x = 5\), it's multiplication by 5.
  • Apply the inverse operation to both sides of the equation; the inverse of multiplication by 5 is division by 5.
  • Dividing both sides by the same number keeps the equation balanced, leading us to \(x = 1\).
After performing these steps, we've successfully isolated \(x\) on one side, which means the equation is set up to reveal the value of \(x\). It's an essential step that brings us closer to solving the equation.
Simplifying Expressions
Simplifying expressions means reducing them to their simplest form. It's a crucial part of solving equations because it makes the math easier to handle and the results clearer to understand. For the equation \(x = \frac{5}{5}\), simplifying it is straightforward because the fraction can be reduced to a whole number. The steps include:
  • Identify the fraction: \(\frac{5}{5}\).
  • Perform the division: 5 divided by 5 equals 1.
Thus, the expression becomes \(x = 1\). By simplifying, we ensure that the answer is as clear and concise as possible, making it simple to verify that it satisfies the original equation. Reducing terms in equations helps prevent errors and aids in understanding the solution process.

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