/*! 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 312 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 312

In the following exercises, solve the equation. $$ -75=1.5 y $$

Short Answer

Expert verified
y = -50

Step by step solution

01

Identify the Equation

Start with the given equation: -75 = 1.5y
02

Isolate the Variable

To solve for y, isolate y by dividing both sides of the equation by 1.5: \(\frac{-75}{1.5} = \frac{1.5y}{1.5}\)
03

Simplify the Equation

Simplify the left side of the equation: \(\frac{-75}{1.5} = y\). Therefore, y = -50.

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.

Isolate the variable
When solving linear equations, the main goal is often to find the value of the variable. To achieve this, you need to isolate the variable on one side of the equation.
In our exercise, the variable is \( y \). The original equation is:\[-75 = 1.5y\]
To isolate \( y \), you need to 'move' 1.5 to the other side. The most common method is to use division.
  • Divide both sides by the coefficient of \( y \), which is 1.5.
The equation becomes:\[\frac{-75}{1.5} = \frac{1.5y}{1.5}\]
This helps to cancel out the 1.5 on the right side, effectively isolating \( y \).
Simplify the equation
Once you've set up the equation to isolate the variable, the next step is to simplify both sides.
In our example, we previously reached the step:\[\frac{-75}{1.5} = y\]
To simplify, perform the division on the left side:
  • \(-75 \div 1.5\)
Simplifying this, we get:
\[-50 = y\]
This means that the value of \( y \) is \(-50\). Simplification helps to reduce the equation and make the solution clearer.
Division in equations
Division is a useful operation when solving equations, especially if you need to isolate a variable. In linear equations, it's common to divide both sides by the coefficient of the variable.
Remember, you must divide both sides of the equation to maintain equality. For example:
If you have \( ax = b \) and you want to solve for \( x \), divide both sides by \( a \):
\[ x = \frac{b}{a} \]
In our exercise, the division step was:
\[-75 = 1.5y\]
Dividing both sides by 1.5, we get:
\[ y = \frac{-75}{1.5} \]
Division here is the key step to isolate \( y \) effectively, leading to the solution \(-50\).

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

approximate the (a) circumference and (b) area of each circle. If measurements are given in fractions, leave answers in fraction form. diameter \(=\frac{3}{4} \mathrm{m}\)

An architect is planning to put a circular mosaic in the entry of a new building. The mosaic will be in the shape of a circle with radius of 6 feet. How many square feet of tile will be needed for the mosaic? (Round your answer up to the next whole number.)

In the following exercises, order each of the following pairs of numbers, using < or >. $$0.7\underline\quad0.8$$

In the following exercises, round each number to the nearest hundredth. $$0.299$$

In the following exercises, translate the English phrase into an algebraic expression. 78 feet per \(r\) seconds
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Pure 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.