Problem 9 Solve each equation, and check y... [FREE SOLUTION]

Chapter 2: Problem 9

Solve each equation, and check your solution. $$ x-6=-9 $$

Short Answer

Expert verified

x = -3

Step by step solution

- Isolate the variable

Add 6 to both sides of the equation to isolate the variable. This gives you: \[ x - 6 + 6 = -9 + 6 \]Simplify to get: \[ x = -3 \]

- Check the solution

Substitute the value of $ x $ back into the original equation to verify it. The original equation is: \[ x - 6 = -9 \]Substitute $ x = -3 $: \[ -3 - 6 = -9 \]Simplify:\[ -9 = -9 \]Since both sides of the equation are equal, the solution is verified as 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, the first goal is to isolate the variable. This means we want to get the variable (like $ x $) all by itself on one side of the equation.
Let's break it down:

We start with the equation $ x - 6 = -9 $.
To isolate $ x $, we need to get rid of the $-6$. How do we do that? By adding 6 to both sides of the equation.

Adding 6 to both sides looks like this:

\[ x - 6 + 6 = -9 + 6 \]

When we add 6 to $-6$, they cancel each other out, leaving us with:

\[ x = -3 \]
Now, the variable $ x $ is isolated. We've found that $ x $ equals $-3$.

Checking Solutions

Now that we have found a value for $ x $, we need to check our solution to make sure it is correct.
This step ensures our initial equation holds true with our found value.
To verify, we'll substitute $ x = -3 $ back into the original equation: $ x - 6 = -9 $.
Let's check it:

Substitute $ x = -3 $ into the original equation:

\[ -3 - 6 = -9 \]
Simplify to get:

\[ -9 = -9 \]
Both sides of the equation are equal, meaning our solution is correct.
Your solution has to satisfy the original equation for it to be correct, and checking your solution is an important step.

Adding to Both Sides

In many equations, adding to both sides is a handy technique. It helps in getting the variable alone by canceling out other numbers.
For instance, in our equation $ x - 6 = -9 $, we needed to get rid of the $-6$.

To do this, we added 6 to both sides of the equation.
Adding the same number to both sides keeps the equation balanced.

Here's the math:

\[ x - 6 + 6 = -9 + 6 \]
It simplifies to:

\[ x = -3 \]
This principle applies to other operations as well. If you need to move a term across the equation, whatever you do to one side, you must do the same to the other side.
This maintains the equality and helps isolate the variable.

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. $$ x-6=-9 $$

Short Answer

Step by step solution

- Isolate the variable

- Check the solution

Key Concepts

Isolate the Variable

Checking Solutions

Adding to Both Sides

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Decision Maths

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.