/*! 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 87 Solve \(2 x-3=8\).... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 87

Solve \(2 x-3=8\).

Short Answer

Expert verified
x = 5.5

Step by step solution

01

Identify the Equation

The given equation to solve is: \[2x - 3 = 8\]
02

- Isolate the Variable Term

First, add 3 to both sides of the equation to eliminate the constant term on the left side.\[2x - 3 + 3 = 8 + 3\]This simplifies to:\[2x = 11\]
03

- Solve for the Variable

Next, divide both sides of the equation by 2 to solve for x.\[\frac{2x}{2} = \frac{11}{2}\]This simplifies to:\[x = \frac{11}{2}\]or in the decimal form,\[x = 5.5\]

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.

isolation of variables
In solving linear equations, one of the first fundamental steps is the isolation of variables. This means we want to get the variable, usually represented by a letter like x or y, alone on one side of the equation.
To do this, we perform operations that will move all other terms to the opposite side. We use addition, subtraction, multiplication, or division to achieve this.
For instance, in the equation \(2x - 3 = 8\), we start by moving the constant (the number without x) to the other side by adding 3 to both sides.
By isolating the variable, we make it easier to find its value.
addition property of equality
The addition property of equality is a fundamental principle used in solving equations. This property states that if you add the same number to both sides of an equation, the two sides remain equal.
For example, in \(2x - 3 = 8\), we add 3 to both sides to maintain the balance: \(2x - 3 + 3 = 8 + 3\).
This results in \(2x = 11\), removing the constant term from the left side. The equation is still balanced, and we've made progress towards isolating the variable.
division property of equality
The division property of equality is another essential tool in solving equations. This property tells us that if we divide both sides of an equation by the same non-zero number, the equality will still hold.
Using the previous result \(2x = 11\), we can simplify it further by dividing both sides by 2: \(\frac{2x}{2} = \frac{11}{2}\).
This results in \(\frac{11}{2}\) or 5.5 as the solution for x. By applying the division property of equality, we find the variable's value and solve the equation.

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. $$(3 x-4)^{2}+(4 x+1)^{2}=(5 x+2)^{2}$$

How many quarts of a \(20 \%\) alcohol solution and how many quarts of pure alcohol should be mixed together to obtain 100 quarts that contain \(30 \%\) alcohol?

$$\text { Solve }-5|x-4|=0$$

A pharmacist has 200 milliliters of a solution that is \(40 \%\) active ingredient. How much pure water should she add to the solution to get a solution that is \(25 \%\) active ingredient?

Solve each equation. $$0.1 x-0.05(x-20)=1.2$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.