/*! 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 12 Solve each inequality and give a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 12

Solve each inequality and give a reason for each step in the solution. $$-2 y > 10$$

Short Answer

Expert verified
y < -5

Step by step solution

01

- Isolate the variable

To isolate the variable, divide both sides of the inequality by -2. Remember to flip the inequality sign when dividing by a negative number.
02

- Divide both sides

Divide -2y by -2 and 10 by -2, resulting in: -2y/-2 < 10/-2
03

- Simplify

Simplify the result of the division to get: 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.

Inequality Solving Steps
Solving an inequality involves a series of steps. Let's look at the provided example step by step: -2y > 10. The first step in solving this is to isolate the variable, y. We do this by performing algebraic operations on both sides of the inequality. Here, we divide both sides by -2 to get -2y/-2 < 10/-2. Notice that the inequality sign flips because we are dividing by a negative number. The final step is to simplify the terms to get y < -5. Remember, each step should logically follow from the previous one and it's crucial to maintain the balance of the inequality at all times.

Summarizing:
  • Isolate the variable by performing algebraic operations on both sides.
  • Ensure balance while performing any operations.
  • Be mindful of special rules like flipping the inequality sign when dividing by a negative number.
Negative Numbers in Inequalities
Dealing with negative numbers in inequalities adds an extra layer of complexity. In our example -2y > 10, we needed to divide by -2 to isolate y. A key rule to remember is that whenever you multiply or divide both sides of an inequality by a negative number, you must flip the sign of the inequality. So, from -2y > 10, the process of dividing by -2 results in y < -5, not y > -5.

This rule exists because of how negative numbers interact with the number line. If we ignored this rule, we'd end up with an answer that doesn't correctly represent the original condition. Therefore, always remember:
  • Division or multiplication by a negative number requires flipping the inequality sign.
  • Apply this rule consistently to maintain the accuracy of your solution.
Algebraic Manipulation
Algebraic manipulation is at the heart of solving any inequality. It's about using algebraic operations to simplify and solve for the variable. Let's look at -2y > 10: We isolate y by dividing both sides by -2. This operation is straightforward: divide -2y by -2 and 10 by -2, which involves basic division.

Simplifying algebraic expressions means performing operations like addition, subtraction, multiplication, and division to isolate the variable. Always perform the same operation on both sides to maintain the balance of the equation or inequality. Here are key points:
  • Identify the operation needed to isolate the variable.
  • Apply the operation equally to both sides.
  • Simplify the expression to get your final answer.

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

The sides of a triangle are in the ratio of \(3: 4: 5 .\) If the perimeter is 90 centimeters, find the lengths of each side.

Write ratio as a fraction and simplify. 18 to 54

In Exercises \(9-14\), is the triangle with sides of the given lengths a right triangle? \(15 \mathrm{ft}, 36 \mathrm{ft}, 39 \mathrm{ft}\)

Solve each inequality and give a reason for each step in the solution. $$1-3 x < 8$$

Prove that the sum of the lengths of the line segments drawn from any point inside a triangle to the vertices is greater than one-half the perimeter of the triangle.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

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.