Chapter 2: Q.32. (page 112)

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$15 y + 32 = 2 (10 y - 7) - 5 y + 46$

Short Answer

Expert verified

The equation is an identity and the solution of this equation is "all real numbers".

Step by step solution

Step 1. Given information.

The given equation is $15 y + 32 = 2 (10 y - 7) - 5 y + 46$ .

Step 2. Apply the distributive property.

Simplify the equation.

$15 y + 32 = 2 \times 10 y - 2 \times 7 - 5 y + 46 15 y + 32 = 20 y - 14 - 5 y + 46 15 y + 32 = 15 y + 32$

Step 3. Collect all variables terms on one side of the equation.

Subtract $15 y$ from each side.

$15 y + 32 - 15 y = 15 y + 32 - 15 y 32 = 32$

This is a true statement.

It means the equation is true for any value of the variable.

So, the equation is an identity.

Hence, the solution of this equation is "all real numbers".

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$15 y + 32 = 2 (10 y - 7) - 5 y + 46$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the distributive property.

Step 3. Collect all variables terms on one side of the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.15y+32=210y-7-5y+46

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the distributive property.

Step 3. Collect all variables terms on one side of the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Logic and Functions

Geometry

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$15 y + 32 = 2 (10 y - 7) - 5 y + 46$