/*! 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 57 Determine whether the given numb... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 57

Determine whether the given number is a solution of the given equation. $$ 93 ; a-28=75 $$

Short Answer

Expert verified
93 is not a solution.

Step by step solution

01

- Understand the Equation

The given equation is written as: \[ a - 28 = 75 \] We need to determine whether the number 93 is a solution to this equation.
02

- Substitute the Given Number

Replace the variable \( a \) with the given number (93) in the equation. This gives us: \[ 93 - 28 = 75 \]
03

- Perform the Subtraction

Calculate the left-hand side of the equation: \[ 93 - 28 = 65 \]
04

- Compare Both Sides

Compare the result from the left-hand side with the right-hand side value. \( 65 eq 75 \)
05

- Conclusion

Since the left-hand side is not equal to the right-hand side, the number 93 is not a solution to the equation \( a - 28 = 75 \).

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.

Equation Substitution
Equation substitution involves replacing a variable in an equation with a given number or value. In this exercise, we substitute the variable \( a \) with 93. This leads to a new equation, which helps us check if 93 is the solution. Think of substitution as temporarily changing the equation to see if the new statement still holds true.
You can follow these steps for substitution:
  • Identify the variable in the original equation.
  • Replace the variable with the given number.
  • Proceed with arithmetic operations to simplify the equation.
Solving for a Variable
Solving for a variable means finding the value of the unknown that makes the equation true. In our exercise, the unknown is \( a \), and we need to verify if 93 is its correct value. To do this, we:
  • Substitute 93 for \( a \) in the equation \( a - 28 = 75 \).
  • Simplify the equation to check if both sides are equal.
If the simplified equation is true, then 93 is the solution. If not, it means 93 is not the solution. This process helps us confirm or refute potential solutions.
The main goal is to isolate the variable on one side of the equation. By carefully manipulating the equation, we can see if our substituted value satisfies the original equation.
Basic Algebra
Basic algebra provides the fundamental rules and operations used to manipulate algebraic expressions and equations. It includes addition, subtraction, multiplication, division, and understanding equality. In this exercise, subtracting 28 from 93 is an example of simple arithmetic within the algebraic process.
To successfully solve algebra problems, these skills are crucial:
  • Identify and understand the variables and constants.
  • Use arithmetic operations to manipulate equations.
  • Keep equations balanced by performing the same operation on both sides.
  • Evaluate whether the final results satisfy the original equation.
Basic algebra serves as the building blocks for more advanced math concepts and problem-solving strategies. By mastering these essentials, solving more complex problems becomes easier and more intuitive.

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

Given that \(0.3 \overline{3}=\frac{1}{3}\) and \(0.6 \overline{6}=\frac{2}{3},\) express each of the following as a ratio of two integers. $$0.9 \overline{9}$$

Evaluate using a calculator. $$ \frac{1}{2}(x+5 / z)^{2}, \text { for } x=141 \text { and } z=0.2 $$

Translate to an inequality. The distance from \(t\) to 0 is at least \(20 .\)

SYNTHESIS Write the sentence \(-|x| \neq-x\) in words. Explain why \(-|x|\) and \(-x\) are not equivalent.

Write an equivalent expression without using grouping symbols. $$ -(3 x+5) $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

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.