/*! 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 104 Determine whether the given numb... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 104

Determine whether the given number is a solution of the equation. $$5(7-z)+12 z=0 ;-5$$

Short Answer

Expert verified
-5 is not a solution to the equation \(5(7-z)+12 z=0\).

Step by step solution

01

Substitute Given Number into the Equation

Substitute \(-5\) for \(z\) in the equation:\[5(7 - (-5)) + 12 (-5) = 0\]
02

Simplify the Equation

This simplifies to \(-60 = 0\]. Both sides of the equation are not equal, hence \(-5\) is not a solution to the equation.
03

Conclude the Solution

-5 does not satisfy the equation \(5(7-z)+12 z=0\), so it is not a solution.

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.

Solution Verification
Solution verification is crucial in solving algebraic equations as it helps us confirm whether a guessed or given value truly satisfies the equation. In simple terms, verification involves checking if substituting the number back into the equation makes both sides equal.

To verify a solution, take the proposed number and replace the variable in the original equation with this number. Once the substitution is done, calculate both sides of the equation. If both sides are equal, then the number is indeed a solution. If they are not equal, as in this particular problem where \(-60 eq 0\), it means the number is not a solution.
  • Verify by substituting the number into the equation.
  • Calculate both sides after substitution.
  • Check for equality to confirm if the number is a solution.
Substitution Method
Substitution is a fundamental method in algebra used to solve and verify equations. It involves replacing variables with given numbers or expressions to simplify the equation.

In our exercise, substitution was employed when the given number, \(-5\), was substituted into the equation \(5(7-z)+12z=0\). This transforms the equation from one involving a variable into a simple arithmetic operation:\[5(7-(-5))+12(-5) = 0\].

By substituting, we convert the equation into a form that can be easily solved or verified to check if both sides match. The substitution method often marks the first step in assessing whether a given number is a potential solution.
Equation Simplification
Simplifying an equation is all about making it easier to handle by reducing it to the simplest form. This often involves combining like terms, removing brackets, and resolving operations.

During simplification, as seen in our problem, the expression \(5(7-(-5))+12(-5)\) becomes more straightforward:
  • First, interpret the sign within the brackets (7 - (-5)) to (7 + 5) = 12.
  • Then multiply through: 5(12) = 60.
  • Add the second part: 12(-5) = -60.
At the end, the simplified equation becomes \(-60 = 0\), revealing that the left side doesn鈥檛 equal the right side, thus verifying that the number -5 is not a solution. Simplification is not just key in making calculations more straightforward, but also in understanding the relationship between different components in an 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

Simplify each series of additions and subtractions. $$-1.9-3-(-0.26)$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can find the closing price of stock PQR on Wednesday by subtracting the change in price, \(-1.23,\) from the closing price on Thursday, 47.19

Perform the indicated subtraction. $$5.7-3.3$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. The quotient of \(-7\) and a number, subtracted from the quotient of \(-12\) and the number.

Perform the indicated subtraction. $$3 \pi-(-10 \pi)$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Applied 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.