/*! 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 144 Translate to an equation and the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 144

Translate to an equation and then solve. -184 is the product of 23 and \(p\).

Short Answer

Expert verified
The value of \(p\) is -8.

Step by step solution

01

- Understand the Problem

The given statement says that -184 is the product of 23 and another number denoted by the variable \(p\). This means the equation will involve multiplication.
02

- Translate the Problem into an Equation

Translate the statement into a mathematical equation. 'The product of 23 and \(p\)' can be written as \(23 \cdot p\). Therefore, the equation is \(-184 = 23 \cdot p\).
03

- Solve the Equation for \(p\)

To find the value of \(p\), isolate \(p\). Divide both sides of the equation by 23: \(-184 / 23 = p\).
04

- Calculate the Value

Perform the division to get: \(-184 / 23 = -8\). So, \(p = -8\).

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 in equations
Multiplication appears often in equations, linking variables and constants. When you see 'the product of' in a problem, this means you'll multiply the given numbers. For example, in our exercise, 'the product of 23 and \( p \)' translates to \(23 \cdot p\). Here, 23 is multiplied by a variable \( p \), creating a product. Multiplication can help model real-world relationships in an equation format.

Understanding this helps you interpret phrases correctly. Remember, the order in multiplication doesn't matter: \(23 \cdot p\) is the same as \(p \cdot 23\). Practice translating similar phrases to sharpen your skills.
isolating variables
Isolating variables means getting the unknown variable on one side of the equation by itself. This is crucial for solving equations. Let's illustrate with our exercise.

We started with the equation \(-184 = 23 \cdot p\). To isolate \( p \), we need to remove the 23 from beside it. In this case, we do the opposite of multiplication, which is division.

Think of isolating the variable like undoing an equation step-by-step: if multiplication is applied, use division, and vice versa. This keeps the equation balanced, like a scale. Understanding how to isolate variables provides the foundation for solving more complex equations in algebra.
division in equations
When isolating a variable, division often comes into play. Consider our equation \(-184 = 23 \cdot p\). To solve for \( p \), we must get \( p \) alone. This means dividing both sides by 23. Thus:

\[ p = \frac{-184}{23} \]

Division helps simplify an equation to solve for the variable. It's important to perform division carefully, ensuring accuracy. Here, dividing -184 by 23 gives us \(-8\), so \( p = -8 \).

Division in equations reverses multiplication, vital in algebraic manipulation. Once you master this, you'll handle more equations confidently.

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

Graph each inequality on the number line and write in interval notation. (a) \(\quad x \leq 5\) (b) \(\quad x \geq-1.5\) (c) \(x<-\frac{7}{3}\)

Solve each equation using the Division and Multiplication Properties of Equality and check the solution. $$-u=15$$

Solve the following equations with variables and constants on both sides. $$11-\frac{1}{5} a=\frac{4}{5} a+4$$

Solve the following equations with variables and constants on both sides. $$8 x-15=7 x+3$$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$6 y<48$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

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.