/*! 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 24 Solve each equation. Check your ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 24

Solve each equation. Check your solution. $$k-4.1=-9.38$$

Short Answer

Expert verified
The solution to the equation is \( k = -5.28 \).

Step by step solution

01

Isolate the Variable

To solve the equation \( k - 4.1 = -9.38 \), the first step is to isolate the variable \( k \). We can do this by adding 4.1 to both sides of the equation. This gives us:\[ k - 4.1 + 4.1 = -9.38 + 4.1 \]This simplifies to:\[ k = -9.38 + 4.1 \]
02

Simplify the Equation

Now, we need to perform the addition on the right side of the equation:\[ -9.38 + 4.1 = -5.28 \]Thus, the value of \( k \) is:\[ k = -5.28 \]
03

Check the Solution

To verify the solution, substitute \( k = -5.28 \) back into the original equation \( k - 4.1 = -9.38 \):\[ -5.28 - 4.1 = -9.38 \]Perform the subtraction on the left side:\[ -5.28 - 4.1 = -9.38 \]This confirms that both sides of the equation are equal, verifying our solution is correct.

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.

Isolating Variables
When solving equations, isolating the variable is the first key step. It involves rearranging the equation so that the variable you're trying to solve for stands alone on one side. To do this effectively, you often use the opposite operation of what's currently being applied to the variable. For example, in the equation \( k - 4.1 = -9.38 \), the operation affecting \( k \) is subtraction by 4.1. To isolate \( k \), you undo this subtraction by adding 4.1 to both sides of the equation:
  • Add 4.1 to both sides: \( k - 4.1 + 4.1 = -9.38 + 4.1 \).
  • This simplifies to \( k = -9.38 + 4.1 \).
Each equation is like a balance scale. By performing the same operation on both sides, you maintain balance and move closer to finding the value of the variable.
Checking Solutions
After finding a potential solution, it's important to check if it's correct by substituting the solution back into the original equation. This step ensures that no mistakes were made during calculations. Let's see how it's done for the example \( k = -5.28 \):
  • Substitute the value back: \( k - 4.1 = -9.38 \) becomes \( -5.28 - 4.1 = -9.38 \).
  • Perform the subtraction: \( -5.28 - 4.1 = -9.38 \).
Since both sides of the equation are equal, the solution is verified.
Correctly checking your work avoids errors and confirms your understanding of the problem-solving process.
Simplifying Equations
Simplifying equations is about performing arithmetic to make equations more manageable. This might involve combining like terms or performing operations to simplify expressions. In our example, once we isolate \( k \) in the equation \( k = -9.38 + 4.1 \), the next step is:
  • Perform the addition: \( -9.38 + 4.1 = -5.28 \).
This operation gives the value of \( k \), making the equation more straightforward:
\( k = -5.28 \). Simplification reveals the solution in the clearest form and finalizes the result obtained by isolating the variable.

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

Solve each equation. Check your solution. $$8=\frac{2}{3} d$$

Write \(\frac{12 n^{2}}{3 a n}\) in simplest form.

The product of \(\frac{8}{15}\) and \(\frac{3}{8}\) is a number _____. \(\mathbf{F}\) between 0 and 1 G between 1 and 2 H between 2 and 3 J greater than 3

Find each sum. $$(-2)+5+(-3)$$

Solve each equation. Check your solution. $$n-4.72=7.52$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

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.