/*! 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 299 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 299

In the following exercises, solve the equation. $$ x-0.4=-3.9 $$

Short Answer

Expert verified
x = -3.5

Step by step solution

01

Understand the Equation

The given equation is \( x - 0.4 = -3.9 \). We need to solve for \( x \).
02

Isolate the Variable

Add 0.4 to both sides of the equation to isolate \( x \). \( x - 0.4 + 0.4 = -3.9 + 0.4 \)
03

Simplify

Simplify both sides of the equation to find the value of \( x \). \( x = -3.5 \)

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 the Variable
In solving linear equations, isolating the variable means getting the unknown variable (like x) by itself on one side of the equation. This step is crucial because it brings us closer to finding the solution. To isolate the variable, we perform operations that cancel out the terms attached to it. For instance, in our equation, we have:

$$ x - 0.4 = -3.9 $$

Here, x is the variable we want to isolate. We notice that 0.4 is being subtracted from x. So, to isolate x, we do the opposite operation鈥攁ddition.

By adding 0.4 to both sides:

$$ x - 0.4 + 0.4 = -3.9 + 0.4 $$

We eliminate the -0.4 on the left side and simplify the right side, moving us closer to the final solution!
Simplifying Equations
Simplifying an equation involves performing arithmetic operations to combine like terms and reduce the expression. It's like cleaning up to make things easier to see and understand. In our example, after isolating the variable, we simplify both sides of the equation:

$$ x - 0.4 + 0.4 = -3.9 + 0.4 $$

The left side simplifies to just x, as -0.4 and +0.4 cancel each other out:

  • Original Left Side: $$x - 0.4 + 0.4$$
  • Simplified Left Side: $$x$$

Next, we simplify the right side by performing the addition:

$$ -3.9 + 0.4 = -3.5 $$

So the equation after simplification is:

$$ x = -3.5 $$

This is our solution!
Pre-Algebra Concepts
Pre-algebra studies lay the foundation for all higher math. It involves understanding basic arithmetic and initial algebraic concepts. Often, students encounter linear equations like the one we solved:

$$ x - 0.4 = -3.9 $$

Key pre-algebra skills include:
  • Identifying variables鈥攕ymbols that represent unknown values.
  • Understanding operations鈥攊nvolving addition, subtraction, multiplication, and division.
  • Executing inverse operations鈥攖o isolate variables and solve equations.

    • In our problem, the concept of inverse operations is paramount: we added 0.4 to negate -0.4 to isolate x. Simplifying each step ensures a clear path to the solution. Returning to basics like inverse operations strengthens comprehension for more complex algebra.

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

In the following exercises, order each of the following pairs of numbers, using < or >. $$0.7\underline\quad0.8$$

In the following exercises, convert each decimal to a fraction or mixed number. $$2.482$$

An architect is planning to put a circular mosaic in the entry of a new building. The mosaic will be in the shape of a circle with radius of 6 feet. How many square feet of tile will be needed for the mosaic? (Round your answer up to the next whole number.)

In the following exercises, translate the English phrase into an algebraic expression. \(j\) beats in 0.5 minutes

approximate the (a) circumference and (b) area of each circle. If measurements are given in fractions, leave answers in fraction form. radius \(=\frac{5}{12}\) yard
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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.