/*! 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 38 Solve each equation using the ad... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 38

Solve each equation using the addition property of equality. Be sure to check your proposed solutions. $$\frac{7}{3}=-\frac{5}{2}+z$$

Short Answer

Expert verified
The solution to the equation is \( z = \frac{29}{6} \)

Step by step solution

01

Rewrite the equation for clarity

First, let's rewrite the equation to make it clearer.\[ \frac{7}{3} = -\frac{5}{2} + z \]
02

Use the Addition Property of Equality to isolate z

To isolate the z term, we'll use the rule of equality which states that we can add the same amount to both sides of an equation without changing its balance. So, add \( \frac{5}{2} \) to both sides of the equation.\[ \frac{7}{3} + \frac{5}{2} = z \]
03

Simplify the equation to find the value of z

Then, calculate the addition on the left side. Make sure both fractions have the same denominator.\[ z = \frac{14}{6} + \frac{15}{6} = \frac{29}{6}\]
04

Check the solution

Finally, substitute \( z = \frac{29}{6} \) into the original equation to confirm the correct solution. The left-hand side becomes \( \frac{7}{3} \), and the right-hand side becomes \( -\frac{5}{2} + \frac{29}{6} = \frac{7}{3} \), so the equation is valid.

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.

Understanding Fractions
Fractions represent parts of a whole and are composed of two main parts: a numerator (the top number) and a denominator (the bottom number). When dealing with fractions, understanding how to find a common denominator is crucial, especially for addition and subtraction.
  • To add fractions, ensure they have the same denominator.
  • Multiply the numerators and denominators accordingly to convert them.
  • Once converted, add the numerators and keep the denominator the same.
In the example given, the fractions \( \frac{7}{3} \) and \( \frac{5}{2} \) needed a common denominator. Both 6 is the least common multiple of 3 and 2, converting them to \( \frac{14}{6} \) and \( \frac{15}{6} \) respectively.
Solving Equations
Solving equations means finding what value the variable represents in order to make the equation true. Equations often involve operations like addition, subtraction, multiplication, and division.
  • Start by simplifying each side of the equation if needed.
  • Use balance methods to keep the equation equal and solve for the variable.
  • Check your solution by plugging it back into the original equation.
In our exercise, the equation is centered around isolating the variable \( z \). By adding \( \frac{5}{2} \) to both sides, we maintain equality, allowing us to solve for \( z \). The result, \( z = \frac{29}{6} \), checks out when substituted back, verifying our solution.
The Substitution Method
The substitution method involves replacing a variable with a known value to check if an equation holds true. It's a validation step for your solution.
  • Identify the solution for the variable from the solved equation.
  • Insert the known solution back into the original equation.
  • Check if both sides of the equation balance.
Once we solved for \( z \) and found \( z = \frac{29}{6} \), we substituted it back into the original equation. Replacing \( z \) with \( \frac{29}{6} \) gives both sides an equal value of \( \frac{7}{3} \), confirming our solution is accurate.

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

Is 4 a solution of \(3 x-14=-2 x+6 ?\)

8 is \(40 \%\) of what number?

An American football field is a rectangle with a perimeter of 1040 feet. The length is 200 feet more than the width. Find the width and length of the rectangular field.

A repair bill on a sailboat came to 1603, dollars including 532 dollars for parts and the remainder for labor. If the cost of labor is 63 dollars per hour, how many hours of labor did it take to repair the sailboat?

Write an original word problem that can be solved using a linear equation. Then solve the problem.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.