Problem 40 Simplify. $$3 y+(-12 x)-7 y+2 ... [FREE SOLUTION]

Chapter 4: Problem 40

Simplify. $$3 y+(-12 x)-7 y+2 y$$

Short Answer

Expert verified

The simplified version of the expression $3 y + (-12 x) - 7 y + 2 y$ is $-12 x -2 y$.

Step by step solution

Identify Like Terms

In the expression $3 y + (-12 x) - 7 y + 2 y$, we can see that $3 y$, $-7 y$, and $2 y$ are like terms because all of them are multiples of 'y'. They can be combined.

Combine Like Terms

When we combine all terms related to 'y', we will add $3 y$, subtract $7 y$ and then add $2 y$. This results in a total of $-2 y$.

Final Simplified Expression

-12x remains as it is since there's no other 'x' term to combine. So, The final simplified form is $-12 x -2 y$.

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.

Like Terms

When you encounter an algebraic expression, one of the first things you should do is identify like terms. Like terms are terms that have the same variables raised to the same powers. This means the variables and their exponents must match exactly. If you look at the example algebraic expression $3y + (-12x) - 7y + 2y$, you can identify

$3y$
$-7y$
$2y$

as like terms because each term contains the variable 'y' raised to the power of one (implicitly). It doesn't matter what coefficients (the numbers in front of the variables) are attached to these variables. Only the variables themselves need to match for the terms to be "like".

Combining Like Terms

Once you have identified the like terms in an algebraic expression, the next step is to combine them. Combining like terms simply means adding or subtracting their coefficients, while keeping the common variable part unchanged. Let's revisit the example expression, $3y + (-12x) - 7y + 2y$. To combine the like terms related to 'y', follow these steps:

Add the coefficients of $3y$ and $2y$: 3 + 2 = 5.
Subtract the coefficient of $-7y$: 5 - 7 = -2.

After combining the coefficients, you'll notice that the variable part 'y' remains unchanged, and you'll arrive at a simpler form of the y-terms: $-2y$. Remember, terms involving 'x', like $-12x$, are left alone if there are no other 'x' terms to combine with.

Algebraic Expression

An algebraic expression is a combination of numbers, variables, and operations (like addition and subtraction) without an equality sign. Unlike equations, algebraic expressions do not have a "left-side equals right-side" structure. Instead, they are like mathematical phrases that suggest a sequence of calculations. For example, the expression $3y + (-12x) - 7y + 2y$ is composed of:

Terms, such as $3y$, $-12x$, $-7y$, and $2y$.
Operations, which include addition and subtraction.
Variables, which are 'y' and 'x' in this case.

These expressions can be simplified by combining like terms as explained before. This process doesn't solve for any particular value, but it makes expressions easier to work with, especially in more complex calculations or when solving equations.

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

Simplify. $$3 y+(-12 x)-7 y+2 y$$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Final Simplified Expression

Key Concepts

Like Terms

Combining Like Terms

Algebraic Expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Geometry

Mechanics Maths

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.