/*! 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 35 Solve the equations and inequali... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 35

Solve the equations and inequalities. $$0.7 x+0.4 x=5.5$$

Short Answer

Expert verified
The value of \( x \) is 5.

Step by step solution

01

Combine Like Terms

Add the coefficients of the variable on the left side of the equation.\( 0.7x + 0.4x = (0.7+0.4)x = 1.1x \). The equation simplifies to: \( 1.1x = 5.5 \).
02

Isolate the Variable

Divide both sides of the equation by 1.1 to solve for \( x \): \( \frac{1.1x}{1.1} = \frac{5.5}{1.1} \). This simplifies to: \( x = 5 \).

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.

Combining Like Terms
When solving linear equations, a crucial step is to combine like terms. Like terms are terms that contain the same variable raised to the same power. For instance, in the expression \(0.7x + 0.4x\), both terms contain the variable \(x\), making them like terms. Combining like terms simplifies the equation by adding or subtracting the coefficients.
Here, we add \(0.7\) and \(0.4\) to get \(1.1\), hence the equation turns into \(1.1x = 5.5\).
This simplification is essential as it reduces the complexity of the equation, making it easier to solve.
So remember, always look for like terms and combine them to streamline the equation.
Isolating the Variable
Isolating the variable means getting the variable on one side of the equation all by itself. This step makes it straightforward to solve for the unknown.
In our example, after combining the like terms, we have: \(1.1x = 5.5\).
To isolate \(x\), we need to get rid of the coefficient \(1.1\) that is multiplied by \(x\). We do this by dividing both sides of the equation by \(1.1\).
Thus, the operation becomes: \( \frac{1.1x}{1.1} = \frac{5.5}{1.1} \).
Doing the division on both sides leaves us with \(x = 5\).
By isolating the variable, we have successfully solved for \(x\), making it easier to see the solution clearly.
Solving Equations
The final goal in solving linear equations is to find the value of the variable that makes the equation true.
Let's break down the general steps to achieve this:
  • First, simplify both sides of the equation if needed. This might involve clearing parentheses and combining like terms.
  • Next, move all terms containing the variable to one side of the equation and all other terms to the opposite side. This step often involves adding or subtracting terms from both sides.
  • Then, isolate the variable by performing inverse operations (e.g., dividing or multiplying) to get the variable alone.
  • Finally, solve the simplified equation to find the variable's value.
Following these steps helps ensure you solve the equation accurately.
Each step should be performed thoughtfully, checking your work along the way to prevent errors.

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 each of the following exercises, perform the indicated operations. Express your answer as a single fraction reduced to lowest terms. $$\frac{6}{35 a^{2}}+\frac{1}{30 a^{3}}$$

solve the equations and inequalities. \(0.05 x+0.08(x+3,000)=890\)

Set up an equation or inequality and solve the problem. Be sure to indicate clearly what quantity your variable represents. Round to the nearest tenth where necessary. John and Susan leave their homes at 8: 00 A.M., going toward each other along the same route, which is 9 miles long. John walks at 4 mph while Susan jogs at 8 mph. At what time will they meet?

Solve the equations and inequalities. $$\frac{5 x-1}{2}-\frac{x-2}{5}=\frac{8 x+11}{6}$$

Solve the equations and inequalities. $$0.155 x+0.075(80-x)=8.4$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

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.