Problem 73 Clear parentheses and combine li... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 3: Problem 73

Clear parentheses and combine like terms. $$5(t-6)+2$$

Short Answer

Expert verified

5t - 28

Step by step solution

Expand the Parentheses

Distribute the 5 across the terms inside the parentheses. This means multiplying 5 by both t and -6.We get: ewline 5(t) + 5(-6) + 2.

Simplify the Expanded Form

Now perform the multiplications: ewline 5t - 30 + 2.

Combine Like Terms

Combine the constant terms -30 and +2 to simplify the expression which results in: ewline 5t - 28.

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.

distributive property

The distributive property is a fundamental concept in prealgebra that allows us to multiply a single term by each term within a set of parentheses. It states that for any numbers or variables, the expression $a(b + c)$ is equal to $ab + ac$. Here's how it works in our exercise:
When we have \[5(t - 6) + 2\], we distribute the 5 to both $t$ and $-6$.
So, we get:
\[5 \times t + 5 \times (-6) + 2\]
Which simplifies further to:
\[5t - 30 + 2\]
The distributive property helps in breaking down complex algebraic expressions, making them easier to handle and simplify.

simplifying expressions

Simplifying expressions involves combining like terms and performing arithmetic operations to reduce an expression to its simplest form. It makes the expression easier to understand and work with.
In our exercise, after using the distributive property, we got the expression:
\[5t - 30 + 2\]
We need to combine like terms to simplify this further. The like terms here are the constants $-30$ and $2$.
Combining $-30 + 2$ results in $-28$.
So, the simplified expression is:
\[5t - 28\]
Simplifying expressions is crucial in algebra as it helps in solving equations and understanding functions more effectively.

prealgebra

Prealgebra is the foundation of all higher-level math, and it's where students first encounter variables, expressions, and basic algebraic techniques. It covers fundamental concepts such as:

Operations with numbers
Solving simple equations
Understanding properties like the distributive property

In our exercise, we use several prealgebra skills:

Applying the distributive property
Performing multiplication and addition/subtraction
Combining like terms

Mastering prealgebra concepts is essential as it sets the stage for more complex mathematics, including algebra, geometry, and calculus. By practicing these foundational skills, students build the confidence and ability to tackle increasingly challenging mathematical problems.

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

Clear parentheses and combine like terms. $$5(t-6)+2$$

Short Answer

Step by step solution

Expand the Parentheses

Simplify the Expanded Form

Combine Like Terms

Key Concepts

distributive property

simplifying expressions

prealgebra

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Statistics

Decision Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.