Problem 14 Solve each equation, and check y... [FREE SOLUTION]

91影视

Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 2: Problem 14

Solve each equation, and check your solution. $$ x+47=26 $$

Short Answer

Expert verified

The solution is x = -21.

Step by step solution

Subtract 47 from both sides

To isolate the variable x, subtract 47 from both sides of the equation: $ x + 47 - 47 = 26 - 47 $

Simplify both sides

Simplify the equation: $ x = 26 - 47 $Calculate 26 - 47: $ x = -21 $

Check your solution

To verify the solution, substitute $ x = -21 $ back into the original equation: $ -21 + 47 = 26 $Simplify the left side: $ 26 = 26 $. The left side equals the right side, so the solution is correct.

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.

Isolate the Variable

When solving linear equations, one of the key steps is to isolate the variable. This means you need to manipulate the equation in a way that gets the variable (in this case, x) by itself on one side of the equation.

Let's look at the original equation: $x + 47 = 26$.

To isolate x, we need to get rid of the 47 on the left side. We do this by performing the same operation on both sides of the equation.

In this case, subtract 47 from both sides: $x + 47 - 47 = 26 - 47$.

This will effectively remove the 47 from the left side, helping us to isolate x. Once we've done that, we have: $x = 26 - 47$.

Now, the variable x is isolated and ready for further simplification.

Simplify Both Sides

After isolating the variable, the next step is to simplify both sides of the equation. Simplifying makes the equation easier to understand and helps in solving it.

From our previous step, we had: $x = 26 - 47$.

Now, simplify the right-hand side: $26 - 47$.

Calculate the difference: $26 - 47 = -21$.

So, we end up with: $x = -21$.

At this point, the simplified equation tells us that x equals -21.

Simplifying both sides helps clarify the value of x and makes it easier to understand the solution.

Check Your Solution

The final step in solving any equation is to check your solution. This step ensures that the value you've found for the variable actually satisfies the original equation.

Let's substitute $x = -21$ back into the original equation $x + 47 = 26$.

Replace x with -21: $-21 + 47 = 26 $.

Simplify the left side: $-21 + 47 = 26$.

Since both sides of the equation are equal $26 = 26$, the solution x = -21 is correct.

Checking your solution is important as it verifies the accuracy of your work and confirms that no mistakes were made during the earlier steps.

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 each equation, and check your solution. $$ x+47=26 $$

Short Answer

Step by step solution

Subtract 47 from both sides

Simplify both sides

Check your solution

Key Concepts

Isolate the Variable

Simplify Both Sides

Check Your Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Probability and Statistics

Calculus

Statistics

Geometry

Study anywhere. Anytime. Across all devices.