/*! 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 232 Solve each linear equation. $$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 232

Solve each linear equation. $$15(y-9)=-60$$

Short Answer

Expert verified
y = 5

Step by step solution

01

- Expand the equation

Distribute the 15 into the parentheses on the left side. This gives: 15(y - 9) = 15y - 135
02

- Set up the equation

Rewrite the equation after expanding: 15y - 135 = -60
03

- Isolate the variable term

Add 135 to both sides of the equation to isolate the 15y term: 15y - 135 + 135 = -60 + 135 This simplifies to: 15y = 75
04

- Solve for y

Divide both sides of the equation by 15 to solve for y: \(y = \frac{75}{15}\) This simplifies to: \(y = 5\)

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.

Expanding Equations
When solving linear equations, the first step often involves expanding equations. This means you need to distribute any constants multiplied by parentheses. In our example, the equation is 15(y - 9) = -60. To expand it, you use the distributive property: multiply 15 by each term inside the parentheses. This becomes 15y - 135. Expanding like this simplifies the problem and makes it easier to work with. Always be sure to distribute to each term within the parentheses.
Isolating Variables
Once you've expanded the equation, the next step is isolating the variable. To isolate means to get the variable (in this case, y) alone on one side of the equation. After expanding, your equation looks like this: 15y - 135 = -60. To isolate the variable term 15y, you need to remove -135. You do this by performing the opposite operation, which is addition in this case. So, add 135 to both sides: 15y - 135 + 135 = -60 + 135. This simplifies to 15y = 75. Remember, whatever you do to one side of the equation, you must do to the other.
Simplifying Equations
The final step in solving the equation is simplifying it to find the value of the variable. We now have 15y = 75. To isolate y, divide both sides by 15: \(y = \frac{75}{15}\). After performing the division, you find that y equals 5. Simplifying equations involves clear arithmetic operations, such as addition, subtraction, multiplication, or division, to simplify the problem and find the variable's exact value. This step is crucial to arrive at the final solution.

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

Translate and solve. Then write the solution in interval notation and graph on the number line. Ten times \(y\) is at most -110 .

Safety A child's height, \(h,\) must be at least 57 inches for the child to safely ride in the front seat of a car. Write this as an inequality.

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$-8 v \leq 96$$

Solve each inequality, graph the solution on the number line, and write the solution in interval notation. $$b+\frac{7}{8} \geq \frac{1}{6}$$

Use the formula \(I=P r t\). Solve for the principal, \(P\) for (a) \(\quad I=\$ 3,950, r=6 \%\) \(t=5\) years (b) in general
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.