/*! 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 58 Find \(x\) in each formula given... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 58

Find \(x\) in each formula given that \(y=2, z=-3,\) and \(w=4\) $$y=\frac{1}{2} w x$$

Short Answer

Expert verified
x = 1

Step by step solution

01

- Substitute the given values into the formula

First, insert the given values for the variables into the formula. The original formula is \[y = \frac{1}{2} w x\]Given values are: \[y = 2, \; w = 4\]Substitute these values into the equation:\[2 = \frac{1}{2} \cdot 4 \cdot x\]
02

- Simplify the equation

Next, simplify the right-hand side of the equation. Calculate \(\frac{1}{2} \cdot 4\):\[2 = 2x\]
03

- Solve for x

Finally, solve for \(x\) by dividing both sides by 2:\[x = \frac{2}{2}\]This simplifies to \[x = 1\]

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.

Substitution in Algebra
Substitution in algebra involves replacing variables with their given numerical values. This technique can simplify complex equations and make it easier to solve for unknown variables.
In our example, we have the formula: \[ y = \frac{1}{2} \, w \, x \] The given values are: \[ y = 2, \; w = 4 \] The first step is to insert the given numerical values for \( y \) and \( w \) into the equation, which makes the equation: \[ 2 = \frac{1}{2} \, 4 \, x \] This simplifies the process and allows us to move on to the next steps with fewer variables.
Simplifying Algebraic Expressions
Simplifying algebraic expressions means reducing them to their simplest forms. This often involves combining like terms, factoring, and performing arithmetic operations. For our example, after substituting the values into the original formula, we had: \[ 2 = \frac{1}{2} \, 4 \, x \] To simplify the right side of the equation, we calculate: \[ \frac{1}{2} \, 4 = 2 \] So the equation now looks like: \[ 2 = 2x \] This step converts the equation into a basic form, which makes it much easier to solve for the unknown variable \( x \).
Solving for a Variable
Solving for a variable means isolating that variable on one side of the equation. This often involves applying algebraic operations like addition, subtraction, multiplication, or division to both sides of the equation. In our last step from the example, we had: \[ 2 = 2x \] To solve for \( x \), we need to isolate \( x \) on one side of the equation. We do this by dividing both sides by 2: \[ x = \frac{2}{2} = 1 \] So, \( x = 1 \). This step confirms the value of \( x \) by simplifying the final expression, showing that \( x = 1 \) satisfies the original 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

Solve each equation. Practice combining some steps. Look for more efficient ways to solve each equation. $$-3-z=3$$

Solve problem by using an inequality. Sewing machines. Charles wants to buy a sewing machine in a city with a \(10 \%\) sales tax. He has at most \(\$ 700\) to spend. In what price range should he look?

Show a complete solution to each problem. Mixed doubles. The doubles court in tennis is one-third wider than the singles court. If the doubles court is 36 feet wide, then what is the width of the singles court?

Show a complete solution to each problem. Really odd integers. If the smaller of two consecutive odd integers is subtracted from twice the larger one, then the result is \(13 .\) Find the integers.

Solve each equation. $$x-0.06 x=50,000$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.