Problem 112 Solve the equation for the varia... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 8: Problem 112

Solve the equation for the variable. $$6 x-2=40$$

Short Answer

Expert verified

x = 7

Step by step solution

Add 2 to Both Sides

To isolate the term with the variable, first add 2 to both sides of the equation:\[6x - 2 + 2 = 40 + 2\]This simplifies to: \[6x = 42\]

Divide by 6

To solve for $ x $, divide both sides of the equation by 6:\[\frac{6x}{6} = \frac{42}{6}\]This simplifies to: \[x = 7\]

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

In algebra, isolating the variable is a crucial step. The main goal is to get the variable you need to solve on one side of the equation. For example, in the equation:
\[6x - 2 = 40\]
You start by removing any constant terms on the same side as the variable. Here, we'll add 2 to both sides to cancel out the -2:
\[6x - 2 + 2 = 40 + 2\]
This simplifies to:
\[6x = 42\]
Now the variable term is isolated, and you can proceed to the next step.

Step-by-Step Solutions

Following a step-by-step approach makes solving equations easier.
1. **Start by identifying what you need to isolate the variable.** In our example:
\[6x - 2 = 40\]
2. **Perform operations on both sides of the equation.** We added 2 to both sides:
\[6x - 2 + 2 = 40 + 2\]
Which simplifies to:
\[6x = 42\]
3. **Next, divide both sides by the coefficient of the variable.** The coefficient of the variable x is 6 in this case:
\[6x/6 = 42/6\]
Which simplifies to:
\[x = 7\]
By breaking down the steps, it becomes clearer how each action moves you closer to the solution.

Basic Algebra

Basic algebra involves understanding and manipulating equations to find unknown values. If you're tackling an equation, remember the following:

Identify and simplify each part of the equation.
Maintain balance by performing the same operations on both sides of the equation.
Use inverse operations to undo terms and coefficients around the variable.

Consider the example:
\[6x - 2 = 40\]
This can be broken down into:

Adding 2 to both sides:

\[6x - 2 + 2 = 40 + 2\]
Which simplifies to:
\[6x = 42\]

Then, dividing by 6:

\[x = 42 / 6\]
Which simplifies to:
\[x = 7\]
With practice, these steps will become intuitive, helping you solve more complex equations efficiently.

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 the equation for the variable. $$6 x-2=40$$

Short Answer

Step by step solution

Add 2 to Both Sides

Divide by 6

Key Concepts

Isolating Variables

Step-by-Step Solutions

Basic Algebra

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Calculus

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.