/*! 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 36 Solve. $$\sqrt{5-x}=1$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 36

Solve. $$\sqrt{5-x}=1$$

Short Answer

Expert verified
x = 4

Step by step solution

01

- Isolate the radical expression

The given equation is \( \sqrt{5-x} = 1 \). The radical expression \( \sqrt{5-x} \) is already isolated on the left side of the equation.
02

- Square both sides of the equation

To eliminate the square root, square both sides of the equation: \( (\sqrt{5-x})^2 = 1^2 \). This simplifies to \( 5 - x = 1 \).
03

- Solve for x

Solve the linear equation obtained in Step 2. Start by isolating \( x \): \( 5 - x = 1 \). Subtract 5 from both sides: \( -x = -4 \). Multiply both sides by -1 to solve for \( x \): \( x = 4 \).
04

- Check the solution

Substitute \( x = 4 \) back into the original equation to verify: \( \sqrt{5-4} = 1 \). Simplifying inside the radical: \( \sqrt{1} = 1 \), which is a true statement. Therefore, \( x = 4 \) is the correct solution.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Radical Equations
A radical equation is any equation that contains a variable within a radical, typically a square root. To solve these types of equations, the goal is to isolate the radical expression and then eliminate it by squaring both sides of the equation. Consider the example:
\ \[ \sqrt{5-x} = 1 \ \]
Here, the radical term \( \sqrt{5-x} \) is already isolated. By squaring both sides of the equation, you get:
\ \[ (\sqrt{5-x})^2 = 1^2 \ \]
Which simplifies to:
\ \[ 5 - x = 1 \ \]
This transformation removes the radical, allowing you to solve the resulting linear equation.
Linear Equations
After breaking down the radical equation, what remains is a linear equation. Linear equations are equations of the first degree, meaning they involve no exponents greater than one. They typically take the form \( ax + b = c \). In our example, we isolated the variable \( x \) as follows:
\ \[ 5 - x = 1 \ \]
To solve, first isolate \( x \). Perform arithmetic operations to both sides of the equation:
  • Subtract 5 from both sides: \( -x = -4 \)
  • Multiply both sides by -1: \( x = 4 \)
By isolating \( x \), a solution of \( x = 4 \) is found. It's important to substitute this solution back into the original equation to verify its correctness.
Step-by-Step Problem Solving
Step-by-Step problem solving is crucial for understanding mathematical concepts deeply. Let's recap the steps used to solve the given equation: The original equation is
  • Step 1 - Isolate the radical expression. The radical \( \sqrt{5-x} \) is already isolated.
  • Step 2 - Square both sides of the equation: \( (\sqrt{5-x})^2 = 1^2 \), leading to \( 5 - x = 1 \).
  • Step 3 - Solve the linear equation. Isolate \( x \):
    • Subtract 5: \( -x = -4 \)
    • Multiply by -1: \( x = 4 \)
  • Step 4 - Check the solution: Substitute \( x = 4 \) into the original equation to verify: \( \sqrt{5-4} = 1 \) simplifies to \( \sqrt{1} = 1 \), confirming the solution is correct.
Using these steps ensures a systematic approach to solving equations, making it easier to catch mistakes and understand each part of the process.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether the statement is true or false. The conjugate of a sum is the sum of the conjugates of the individual complex numbers.

Solve and write interval notation for the solution set. Then graph the solution set. $$|5-2 x|>10$$

Solve. $$\sqrt{x+5}+1=\frac{6}{\sqrt{x+5}}$$

Solve. $$\sqrt{y+4}-\sqrt{y-1}=1$$

Find the zero of the function. $$f(x)=-3 x+9$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.