/*! 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 46 Solve each equation. $$-(k+7)+... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 46

Solve each equation. $$-(k+7)+2 k+8=7$$

Short Answer

Expert verified
k = 6

Step by step solution

01

Distribute the Negative Sign

Distribute the negative sign through the term \(k+7\): \(-(k+7) = -k-7\).
02

Rewrite the Equation

Rewrite the equation after distributing the negative sign. The equation now becomes: \(-k - 7 + 2k + 8 = 7\).
03

Combine Like Terms

Combine the like terms (terms that contain \(k\) and the constant terms): \(-k + 2k - 7 + 8 = 7\). This simplifies to \(k + 1 = 7\).
04

Solve for k

Isolate \(k\) by subtracting 1 from both sides of the equation: \[k + 1 - 1 = 7 - 1\]. This simplifies to \[k = 6\].

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.

Distributing Negative Sign
When solving linear equations, one key step is distributing a negative sign. This means that we apply the negative sign to each term inside the parentheses. For example, in the expression \(-(k+7)\), we distribute the negative across both terms inside the parentheses. Here's how it works: $$-(k+7) = -k - 7$$. By changing the signs of both the terms, we now have $$-k$$ and $$-7$$ instead of $$k$$ and $$7$$. Always remember, when you see a negative sign in front of parentheses, it affects every term inside.
Combining Like Terms
Once you've distributed any necessary negative signs, the next step is combining like terms. Like terms are terms that have the same variable raised to the same power. For instance, in the equation $$-k - 7 + 2k + 8 = 7$$, we combine the like terms: $$-k$$ and $$2k$$. These are like terms because they both contain the variable $$k$$. When we combine them by adding their coefficients (numbers in front of the variables), we get: $$-k + 2k = k$$. Next, combine the constant terms: $$-7$$ and $$8$$, which simplifies to $$-7 + 8 = 1$$. Now our equation looks much simpler: $$k + 1 = 7$$. Always aim to combine like terms to make the equation easier to solve.
Isolating Variable
After combining the like terms, the final key step is isolating the variable. This means rearranging the equation so the variable is by itself on one side. From the simplified equation $$k + 1 = 7$$, we isolate $$k$$ by subtracting $$1$$ from both sides: $$k + 1 - 1 = 7 - 1$$, which simplifies to $$k = 6$$. Isolating the variable makes sure that the solution to the equation is clear. Remember, whatever operation you perform on one side of the equation, you must perform on the other side to keep the equation balanced.

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

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$-25<\frac{p}{-5}$$

Explain why it is necessary to reverse the inequality when solving \(\frac{n}{-3}<12\).

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$9 u+5(2 u-5) \geq 12(u-1)+7 u$$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$6 n-12(3-n) \leq 9(n-4)+9 n$$

Use the formula \(d=r t\). Solve for \(t\) (a) when \(d=350\) and \(r=70\) (b) in general
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.