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Chapter 4: Problem 52

Solve. $$ w+1.3004=47.8 $$

Short Answer

Expert verified
w=46.4996

Step by step solution

01

Identify the equation

The given equation is . This helps to set up the problem for solving.
02

Isolate the variable

To solve for , isolate . Subtract 1.3004 from both sides of the equation: .
03

Perform the subtraction

Perform the subtraction on both sides: . This results in: .

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the Variable
In algebra, isolating the variable is a fundamental step in solving equations. The goal is to get the variable alone on one side of the equation so we can determine its value. This often involves manipulating the equation using inverse operations like addition and subtraction.

In our example, the given equation is:

. Here, we want to get 'w' by itself on one side.

The first step is to identify the operations affecting 'w'. In this case, 'w' is being added to 1.3004. To isolate 'w', we need to
Subtraction in Equations
When solving equations, subtraction is to undo addition. Because 1.3004 is added to 'w', we'll subtract it from both sides to isolate 'w'.

Let's rewrite our initial problem:
. To isolate 'w', subtract 1.3004 from both sides: .

This simplifies to:
. Now, perform the subtraction operation:
. With 'w' isolated, we've solved for its value.
Algebraic Equations
Algebraic equations include variables and constants joined by mathematical operations, like addition or subtraction. Solving these requires understanding how to manipulate the equation to isolate the variable.

Consider our example:
. This equation is linear because the variable 'w' is not raised to any power other than 1.

Using fundamental algebraic principles, we isolate 'w' by working with the constants and eliminating operations on the variable.

By systematically applying the rules of algebra 鈥� such as performing inverse operations 鈥� we can find the value of 'w'.

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Most popular questions from this chapter

You can drive from home to work using either of two routes: Route A: Via interstate highway, \(7.6 \mathrm{mi}\), with a speed limit of \(65 \mathrm{mph}\). Route \(B\) : Via a country road, \(5.6 \mathrm{mi}\), with a speed limit of \(50 \mathrm{mph}\). Assuming you drive at the posted speed limit, which route takes less time? (Use the formula distance \(=\) speed \(\times\) time. \()\)

The Lanosga family's odometer reads 22,456.8 at the beginning of a trip. The family's online driving directions tell them that they will be driving \(234.7 \mathrm{mi}\). What will the odometer read at the end of the trip?

Subtract. $$ \begin{array}{r} 92.341 \\ -\quad 6.42 \\ \hline \end{array} $$

Subtract. $$ \begin{array}{r} 3.4 \\ -0.003 \\ \hline \end{array} $$

One U.S. dollar was worth about 17.7178 Mexican pesos recently. Write a word name for 17.7178
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