Chapter 2: Q.36. (page 112)

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$30 (2 n - 1) = 5 (10 n + 8)$

Short Answer

Expert verified

The equation is a conditional equation and the solution of this equation is $n = 7$ .

Step by step solution

Step 1. Given information.

The given equation is $30 (2 n - 1) = 5 (10 n + 8)$ .

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

$30 \times 2 n - 30 = 5 \times 10 n + 5 \times 8 60 n - 30 = 50 n + 40$

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

Subtract $50 n$ from each side.

$60 n - 30 - 50 n = 50 n + 40 - 50 n 10 n - 30 = 40$

Step 4. Collect all constant terms on one side of the equation and then simplify.

Add 30 to each side.

$10 n - 30 + 30 = 40 + 30 10 n = 70$

Divide each side by $10$ .

$\frac{10 n}{10} = \frac{70}{10} n = 7$

From the above result, we can say that the given equation is true only for $n = 7$ .

So, the equation is a conditional equation.

Hence, the solution of the given equation is $n = 7$ .

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Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.
$30 (2 n - 1) = 5 (10 n + 8)$

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.

Step 4. Collect all constant terms on one side of the equation and then simplify.

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Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.302n-1=510n+8

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.

Step 4. Collect all constant terms on one side of the equation and then simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Logic and Functions

Decision Maths

Discrete Mathematics

Mechanics 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.
$30 (2 n - 1) = 5 (10 n + 8)$