/*! 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 32 Solve the equation using the mul... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 32

Solve the equation using the multiplication or division properties of equality. $$\frac{t}{8}=0$$

Short Answer

Expert verified
t = 0

Step by step solution

01

- Identify the Equation

Start with the equation \(\frac{t}{8} = 0\).
02

- Understand the Goal

The goal is to isolate the variable\( t \). This means getting\( t \) on one side of the equation by itself.
03

- Use Multiplication Property of Equality

To isolate\( t \), multiply both sides of the equation by 8. This step will cancel the denominator: \(8 \times \frac{t}{8} = 8 \times 0\).
04

- Simplify Both Sides

Simplify both sides of the equation: \( t = 0 \). This is because any number multiplied by zero equals zero, and \( \frac{t}{8} \times 8 \) simplifies to \( t \).

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.

Multiplication Property of Equality
When solving equations, the multiplication property of equality is very useful.
This property states that you can multiply both sides of an equation by the same number, and the equality will still hold.
For example, if you have the equation \(\frac{t}{8} = 0\), you can multiply both sides by 8 to isolate the variable.
Multiplying both sides by 8 looks like this:
\[ 8 \times \frac{t}{8} = 8 \times 0 \]
This will help remove the denominator and simplify the equation.
This property is crucial for equations with fractions or coefficients. It maintains the balance, ensuring both sides are equal.
Division Property of Equality
Another essential concept in solving equations is the division property of equality.
This property states that you can divide both sides of an equation by the same non-zero number, and the equality will still hold.
For example, if you have the equation \((4t = 16)\), you can divide both sides by 4 to solve for t:
\[ \frac{4t}{4} = \frac{16}{4} \]
Which simplifies to \((t = 4)\). This property is especially useful when you need to isolate a variable that is multiplied by a constant.
Isolate the Variable
Isolating the variable is often the main goal when solving equations.
This means getting the variable alone on one side of the equation.
For instance, in the equation \(\frac{t}{8} = 0\), we want to isolate \((t)\).
To achieve this, follow these steps:
  • Identify the operation affecting the variable (in this case, division by 8).
  • Apply the opposite operation to both sides (multiplication by 8).
This makes the equation:
\[ t = 0 \]
Isolating the variable makes it easier to understand what value the variable holds.
Simplifying Equations
Simplifying equations is all about making them easier to solve.
It often involves combining like terms or performing operations to both sides of the equation.
In our example, \(\frac{t}{8} = 0\), when we multiply both sides by 8, we get:
\[ t = 8 \times 0 \]
Which simplifies to:
\[ t = 0 \]
Simplifying equations helps you to clearly see the value of the variable.
Always look to perform the same operation on both sides to maintain the equation's balance.

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 the equation. $$6 p=-18$$

Clear parentheses and combine like terms. $$11+2(p-8)$$

Comparing the Properties of Equality In your own words, explain how to determine when to use the subtraction property of equality.

Solve the equation. $$p-6=-18$$

Apply the appropriate property to simplify the expression. $$3+(25-m)$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

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.