Chapter 2: Q.38. (page 112)

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$18 u - 51 = 9 (4 u + 5) - 6 (3 u - 10)$

Short Answer

Expert verified

The equation is a contradiction and the equation has no solution.

Step by step solution

Step 1. Given information.

The given equation is $18 u - 51 = 9 (4 u + 5) - 6 (3 u - 10)$ .

Step 2. Apply the distributive property to simplify the equation.

$18 u - 51 = 9 \times 4 u + 9 \times 5 - 6 \times 3 u + 6 \times 10 18 u - 51 = 36 u + 45 - 18 u + 60 18 u - 51 = 18 u + 105$

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

Subtract $18 u$ from each side.

$18 u - 51 - 18 u = 18 u + 105 - 18 u - 51 = 105 (f a l s e)$

This equation is false for all values of variable.

So, the equation is a contradiction.

Hence, the equation has no solution.

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.
$18 u - 51 = 9 (4 u + 5) - 6 (3 u - 10)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the distributive property to simplify the equation.

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

Geometry

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.18u-51=94u+5-63u-10

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the distributive property to simplify the equation.

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

Geometry

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$18 u - 51 = 9 (4 u + 5) - 6 (3 u - 10)$