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Chapter 2: Q.36. (page 112)

Classify the below equation as a conditional equation, an identity, or a contradiction, and then state the solution.

302n-1=510n+8

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

The given equation is302n-1=510n+8.

02

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

30脳2n-30=5脳10n+5脳860n-30=50n+40

03

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

Subtract 50nfrom each side.

60n-30-50n=50n+40-50n10n-30=40

04

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

Add 30 to each side.

10n-30+30=40+3010n=70

Divide each side by 10.

10n10=7010n=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 isn=7.

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