/*! 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 42 If the exercise is an expression... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 42

If the exercise is an expression, simplify it; if it is an equation, solve it. $$8-3(x-4)=14$$

Short Answer

Expert verified
x = 2

Step by step solution

01

Distribute the -3

Apply the distributive property to the term $$-3(x-4)$$ This gives: $$8 - 3x + 12 = 14$$
02

Combine Like Terms

Combine the constant terms on the left-hand side: $$8 + 12 - 3x = 14$$ This simplifies to: $$20 - 3x = 14$$
03

Isolate the Variable Term

Subtract 20 from both sides to begin isolating the variable term: $$- 3x = 14 - 20$$ simplifying to: $$-3x = -6$$
04

Solve for x

Divide both sides by -3 to solve for x: $$x = \frac{-6}{-3}$$ simplifies to: $$x = 2$$

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 essential to simplify and solve linear equations. It allows you to multiply a single term by each term inside parentheses. In our problem, we apply the distributive property to the term \( -3(x-4) \). This means we multiply -3 by both x and -4.

Let's break this down: \[ -3(x - 4) = -3 \cdot x + (-3) \cdot (-4) \]
After the multiplication, we get: \[ -3x + 12 \] By applying the distributive property correctly, we turn our equation into: \[ 8 - 3x + 12 = 14 \]
This step is crucial as it transforms the equation into a simpler form, making it easier to solve in the subsequent steps.

Combining Like Terms
After the distributive property is applied, we move on to combining like terms. Like terms are terms that have the same variable raised to the same power. In our equation \( 8 - 3x + 12 = 14 \), we need to combine the constants 8 and 12.

Combining like terms simplifies our equation as follows: \[ 8 + 12 - 3x = 14 \] This further reduces to: \[ 20 - 3x = 14 \] Combining like terms helps to consolidate the equation, which makes the isolation of variables easier in the next steps.

Isolating Variables
Isolating the variable is the next crucial step in solving linear equations. Our simplified equation is \( 20 - 3x = 14 \). To isolate the variable term (the term with x), we need to get rid of the constant term on the same side as the variable.

We subtract 20 from both sides to begin the process: \[ 20 - 3x - 20 = 14 - 20 \] This change simplifies the equation to: \[ -3x = -6 \] Now, the variable term is isolated on one side of the equation. This makes solving for x in the final step straightforward.

Solving for x
The last step in solving the equation is to find the value of x. Our equation is now \( -3x = -6 \). To solve for x, we need to get x by itself on one side of the equation.

Since x is being multiplied by -3, we do the opposite operation, which is division. We divide both sides by -3: \[ x = \frac{-6}{-3} \]
Simplifying this gives us: \[ x = 2 \]
This gives us our final solution: x = 2. By following these steps, you can successfully solve linear equations step-by-step, gaining confidence with each concept.

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 of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. Anthropologists often extrapolate the appearance of a human being from the parts of a skeleton they uncover. The following mathematical model relates the height \(h\) (in centimeters) of the individual to the length \(f\) (in centimeters) of the femur (thigh bone): $$h=3.68 f+21.44$$ (a) Use this model to find the height of an individual whose femur measures \(35 \mathrm{cm}\) (b) Use this model to find the length of a femur corresponding to an individual who is \(180 \mathrm{cm}\) tall.

Solve each of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. A trucking company determines that the cost \(C\) (in dollars per mile) of operating a truck is given by \(C=0.003 s+0.21,\) where \(s\) is the average speed of the truck. (a) Find the cost per mile if the truck averages 55 miles per hour. (b) Find the average speed that yields a cost per mile of \(\$ 0.35\)

Perform the indicated operations on the given inequality. Sketch the resulting inequality on a number line. \(2

Perform the indicated operations on the given inequality. Sketch the resulting inequality on a number line. \(-5<-x<-1 ;\) multiply each member by \(-1\)

Solve each of the problems algebraically. That is, set up an equation and solve it. Be sure to clearly label what the variable represents. Round your answer to the nearest tenth where necessary. One of the various models that is proposed for the proper weight \(W\) (in pounds) of a man \(h\) inches tall is \(W=5.7 h-228\) (a) According to this model, what is the proper weight for a person who is 6 feet tall? (b) According to this model, how tall is a person whose proper weight is 200 pounds?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.