/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Simplify each expression. $$(3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 12

Simplify each expression. $$(3+k)+8$$

Short Answer

Expert verified
The simplified expression is \(k + 11\).

Step by step solution

01

Identify like terms

In the expression \((3 + k) + 8\), identify the terms that are numbers and any variable terms. Here, 3 and 8 are numbers or constants, and \(k\) is a variable term.
02

Simplify constants

Add the constant terms in the expression. Calculate \(3 + 8\), which equals 11. This gives us \(11 + k\).
03

Write the simplified expression

Combine the terms to give the simplified expression: \(k + 11\).

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
In algebra, when we talk about 'like terms', we refer to terms within an expression that have identical variable parts. Understanding this is crucial for simplifying expressions effectively.

A like term can include:
  • Only constants, which are numbers without any variables.
  • Variables raised to the same power and multiplied by any constant coefficients.
When simplifying an expression, you can only combine like terms. For example, in the expression \(3x + 4 + 5x + 7\):
  • \(3x\) and \(5x\) are like terms because they both contain the variable \(x\).
  • \(4\) and \(7\) are like terms because they are constants without variables.
Combining like terms helps in reducing the expression to its simplest form, making it easier to understand and work with.
Constants
Constants are the numbers in an expression that do not change. They are the fixed values without any variables attached. In straightforward terms, they are just regular numbers.

For instance, in the expression \(3 + k + 8\):
  • \(3\) and \(8\) are constants because they have no variables that change their value.
When simplifying an expression:
  • Gather and sum all constant terms for simplification.
  • In this exercise, you add \(3\) and \(8\), which equal \(11\).
Combining constants allows you to reduce an expression and make solving equations more straightforward.
Variables
Variables are symbols used to represent unknown or changeable numbers in an expression or equation. The most common letters used for variables are \(x\), \(y\), \(z\), but any letter can serve as a variable. They are essential to forming algebraic expressions.

In the expression \(3 + k + 8\):
  • \(k\) is the variable. It stands for an unknown number that can change depending on the problem's context.
Understanding variables helps in:
  • Solving equations where you need to find the value of the variable.
  • Representing real-life problems and relationships mathematically.
Variables are crucial as they allow us to create formulas and equations to model and solve various mathematical scenarios.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether a scatter plot of the data for the following might show a positive, negative, or no relationship. Explain your answer. size of household and amount of water bill.

Copy each sentence. Then insert parentheses to make each sentence true. $$56 \div 2+6-4=3$$

Write two different equations whose solutions are each 5 .

A telephone tree is set up so that every person calls three other people. Jeffrey needs to tell his co-workers about a time change for a meeting. Suppose it takes 2 minutes to call 3 people. In 10 minutes, how many people will know about the change of time?

Suppose only the 1, +, -, x, \(\div\) (, ), and ENTER keys on a calculator are working. How can you get a result of 75 if you are only allowed to push these keys fewer than 20 times?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.