Question

solve the following linear equation
1) x+(x-2/3)=1+(x-1/2)

Answer 1

$x + ( \frac{x - 2}{3} ) = 1 + ( \frac{x - 1}{2} )$

$x + ( \frac{2x}{3} ) = 1 + ( \frac{1x}{2})$

$\frac{x + 2x}{1 + 3} = \frac{1 + 1x}{1 + 2}$

$\frac{3x}{4} = \frac{2x}{3}$

$\frac{3x + 2x}{4 + 3}$

$\frac{5x}{7}$

$x = \frac{5}{7}$

Answer 2

Answer:

+

x−2

2

=

x−3

3

(x−1)(x−2)

x−2+2(x−1)

=

x−3

3

(x−1)(x−2)

2x+x−2−2

=

x−3

3

(x−3)(3x−4)=3(x−1)(x−2)

3x

2

−9x−4x+12=3(x

2

−3x+2)

3x

2

−13x+12=3x

2

−9x+6

−13x+12=−9x+6

13x−12=9x−6

13x−9x=12−6

4x=6

x=

4

6

=

2

3

∴x=

2

3

.