# To find the real solutions of equation 1 x + 2 x − 1 = 3 . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 76RE
To determine

## To find the real solutions of equation 1x+2x−1=3 .

Expert Solution

The solution is x=±13 .

### Explanation of Solution

Given information:

1x+2x1=3

Formula used:

Properties of fractions:- AC+BC=A+BC .

Distributive property:- a(b+c)=ab+ac

Calculations:

=1x+2(x1)=3

=(x1)x(x1)+2xx(x1)=3 (Re-write in LCD form)

=x1+2xx(x1)=3=3x1x(x+1)=3

=3x1=3(x)(x+1) (by cross - multiplying)

=3x1=3x(x+1)=3x1=3x(x)+3x(1)=3x1=3x2+3x

=3x13x23x=0

=13x2=0 (Subtracting like terms)

=13x2+1=0+1 (Adding 1 on both the sides)

=3x2=1

=3x23=13 (Dividing by (-3) on both the sides)

=x2=13

=x=±13 (Taking under-root both the sides)

The solution of the equation x=±13 .

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