## Algebra: A Combined Approach (4th Edition)

Published by Pearson

# Chapter 7 - Review: 52

#### Answer

The number is $\Longrightarrow$ 2

#### Work Step by Step

Let the number be 'x' Reciprocal of x c $\frac{1}{x}$ Difference of 4 and x = 4 - x Reciprocal $\Longrightarrow$ $\frac{1}{4 - x}$ Given: $\frac{1}{x}$ = $\frac{1}{4 - x}$ Cross multiplying both sides, 1(4 - x) = 1(x) 4 - x = x Adding 'x' on both sides, 4 - x + x = x + x 2x = 4 $\frac{2x}{2}$ = $\frac{4}{2}$ ....(Dividing both sides by 2) Thus x = 2

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