/*! 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 26 For exercises 1-72, (a) solve.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 26

For exercises 1-72, (a) solve. (b) check. $$ 7 x-12=44 $$

Short Answer

Expert verified
x = 8

Step by step solution

01

Isolate the variable term

To isolate the term with the variable, add 12 to both sides of the equation:\[ 7x - 12 + 12 = 44 + 12 \]This simplifies to:\[ 7x = 56 \]
02

Solve for the variable

Divide both sides of the equation by 7 to solve for \(x\):\[ x = \frac{56}{7} \]This simplifies to:\[ x = 8 \]
03

Check the solution

Plug the solution back into the original equation to verify it:\[ 7(8) - 12 = 44 \]Calculate the left side:\[ 56 - 12 = 44 \]Since both sides are equal, the solution is 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
In order to solve for the variable in an equation, always start by isolating the variable term. This means you want to make sure only the term with the variable is on one side of the equation and everything else is on the other side.

For the equation given: \[ 7x - 12 = 44 \]
Firstly, identify any constants or terms that do not contain the variable. In this example, \(-12\) is such a term. To move it to the other side of the equation, perform the opposite operation鈥攊n this case, add 12 to both sides:

\[ 7x - 12 + 12 = 44 + 12 \]
This simplifies to:

\[ 7x = 56 \]
Now, the variable term is isolated, and we can proceed to the next step.
Divide Both Sides
Once the variable term is isolated, the next objective is to solve for the variable itself. This often involves a division step if the variable is being multiplied by a coefficient.

For the isolated equation: \[ 7x = 56 \]
The coefficient of \(x\) is 7. To solve for \(x\), divide both sides by 7:

\[ x = \frac{56}{7} \]
This simplifies to:

\[ x = 8 \]
By dividing both sides by the coefficient, you effectively 'cancel out' the coefficient, leaving the variable \(x\) by itself on one side. Now, you've found the value of the variable, which is 8.
Check the Solution
After finding the variable's value, it's crucial to check the solution to ensure it's correct. This verification step helps confirm accuracy and catches any potential mistakes.

Substitute the value of \(x = 8\) back into the original equation:

\[ 7x - 12 = 44 \]
Substitute \(x = 8\) into the equation:

\[ 7(8) - 12 = 44 \]
Perform the multiplication and subtraction on the left side:

\[ 56 - 12 = 44 \]
Since both sides of the equation are equal \((44 = 44)\), the solution is confirmed to be correct. This step wraps up the process and assures that \(x = 8\) is indeed the solution to the equation.

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

For exercises 93-96, the completed problem has one mistake. (a) Describe the mistake in words, or copy down the whole problem and highlight or circle the mistake. (b) Do the problem correctly. Problem: Solve: \(-2 x+12>36\) Incorrect Answer: \(-2 x+12>36\) $$ \begin{aligned} -12 &-12 \\ \hline-2 x+0 &>24 \\ \frac{-2 x}{-2} &>\frac{24}{-2} \\ x &>-12 \end{aligned} $$

In Sept. 2010, \(1.4\) million people received cash assistance from the California Work Opportunity and Responsibility to Kids (CalWORKS) program. More than three out of four of these recipients were children. Find the minimum number of recipients who were children. (Source: www.lafla.org, Jan 2011)

For exercises 9-36, (a) solve. (b) check the direction of the inequality sign. $$ 4 a-12<60 $$

An athlete needs a final grade of at least 82 (B) in his chemistry class to maintain his athletic eligibility. His final grade is the sum of \(55 \%\) of his test score average, \(25 \%\) of his lab score average, and \(20 \%\) of his final exam score. Before the final, his test score average is 75 , and his lab score average is 88 . Find the score on the final that he needs to have a final grade of at least 82. Round to the nearest whole number.

For problems \(89-92\), do the arithmetic with a calculator. The area \(A\) of a rectangular playground is \(28,800 \mathrm{ft}^{2}\). The length \(L\) is \(180 \mathrm{ft}\). Solve the formula \(A=L W\) for \(L\), and use it to find the width \(W\) of the playground.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

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.