Problem 23 Solve. $$ x+0.45=2.6 x $$... [FREE SOLUTION]

91影视

Chapter 15: Problem 23

Solve. $$ x+0.45=2.6 x $$

Short Answer

Expert verified

x = 0.28125

Step by step solution

Move All Terms with x to One Side

Subtracting both sides by $ x $ to move the $ x $ terms to one side results in:\[ 0.45 = 2.6x - x \]

Combine Like Terms

Simplify the right side by combining like terms:\[ 0.45 = 1.6x \]

Solve for x

Divide both sides by 1.6 to isolate $ x $:\[ x = \frac{0.45}{1.6} \]

Simplify the Fraction

Perform the division to find the value of $ x $:\[ x = 0.28125 \]

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.

solving equations

Solving equations is a fundamental skill in algebra. An equation is a mathematical statement that asserts the equality between two expressions. Your goal is to find the value of the variable that makes the equation true.
Steps to solve an equation often involve rearranging terms, combining like terms, and isolating the variable. This exercise required moving all x terms to one side, combining terms, and isolating x.

combining like terms

Combining like terms is an important step in simplifying equations. Like terms are terms that have the same variables raised to the same power.
For example, in the equation given: $$x + 0.45 = 2.6x$$
Subtracting x from both sides helps move all x terms to one side:$$0.45 = 2.6x - x$$
The x terms on the right side can be combined:
$$0.45 = 1.6x$$

isolating variable x

Isolating the variable x means manipulating the equation such that x is by itself on one side of the equation. When you have an equation like:
$$0.45 = 1.6x$$
You want to solve for x, so you need to get x alone. This is done by dividing both sides of the equation by the coefficient of x, which is 1.6:
$$x = \frac{0.45}{1.6}$$
Make sure to perform the same operation on both sides to maintain the equality.

fractions in equations

Working with fractions in equations can be tricky, but the principle is the same: perform operations to isolate the variable. After combining like terms in the exercise, you have:
$$x = \frac{0.45}{1.6}$$
Performing the division simplifies the fraction to get the solution:
$$x = 0.28125$$
Fractions are common in solving equations, so practice makes perfect. Ensure all steps are clear and operations are performed on both sides of the equation to maintain balance.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve. $$ x+0.45=2.6 x $$

Short Answer

Step by step solution

Move All Terms with x to One Side

Combine Like Terms

Solve for x

Simplify the Fraction

Key Concepts

solving equations

combining like terms

isolating variable x

fractions in equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Pure Maths

Logic and Functions

Calculus

Geometry

Study anywhere. Anytime. Across all devices.