/*! 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 166 Solve the linear equation using ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 166

Solve the linear equation using the general strategy. $$20(y-8)=-60$$

Short Answer

Expert verified
y = 5

Step by step solution

01

Distribute the 20

Multiply 20 by both terms inside the parenthesis: \( 20(y - 8) \). This gives: \( 20y - 160 \). So the equation becomes: \( 20y - 160 = -60 \).
02

Move the constant term to the other side

Add 160 to both sides of the equation to isolate the term with the variable: \( 20y - 160 + 160 = -60 + 160 \). This simplifies to: \( 20y = 100 \).
03

Solve for y

Divide both sides by 20 to solve for \( y \): \( \frac{20y}{20} = \frac{100}{20} \). This gives: \( y = 5 \).

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.

linear equations
Linear equations are mathematical expressions where the highest exponent of the variable is one. They take the general form of \(Ax + B = C\), where \(A\), \(B\), and \(C\) are constants and \(x\) is the variable.

In our exercise, the linear equation is \(20(y-8) = -60\). This is a typical example where we need to solve for \(y\). Equations like this appear frequently in algebra and can be solved using systematic steps.
distributive property
The distributive property allows you to multiply a sum by a number, spreading the multiplication over each term within the parentheses. It is expressed as \(a(b + c) = ab + ac\).

In our problem, we distribute 20 to both \(y\) and \(-8\) inside the parentheses: \(20(y - 8) = 20y - 160\). This property is useful when simplifying equations and making them easier to solve.
isolating variables
Isolating the variable means getting the variable by itself on one side of the equation. This usually involves moving terms with constants to the other side.

For example, after using the distributive property, our equation \(20y - 160 = -60\) needs further simplification. We isolate \(y\) by adding 160 to both sides of the equation, resulting in: \(20y - 160 + 160 = -60 + 160\) simplifies to \(20y = 100\).
solving for a variable
Solving for a variable involves making the variable the subject of the equation. This means performing operations that simplify the equation and solve for the unknown.

At the final step of our problem, the isolated equation is \(20y = 100\). To solve for \(y\), we divide both sides by 20: \(\frac{20y}{20} = \frac{100}{20}\). This results in \(y = 5\).

This systematic approach ensures you accurately find the value of the variable.

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

In the following exercises, solve the equations with constants on both sides. $$ 32=-4-9 n $$

In the following exercises, solve each equation. $$ 10 y=-5 y+60 $$

In the following exercises, solve each equation. $$ 4 y-8=16 $$

In the following exercises, translate into an equation and solve. Pablo鈥檚 father is 3 years older than his mother. Pablo鈥檚 mother is 42 years old. How old is his father?

In the following exercises, solve each equation. $$ 6(9 y-1)-10(5 y)-3 y=22 $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.