Zad.: Nr 12:
a ) x/3 + 1 = ⅚ + x/2
⅓ x + 1 = ⅚ + ½ x / - ½ x - 1
⅓ x - ½ x = ⅚ - 1
2/6 x - 3/6 x = ⅚ - 1
-⅙ x = ⅚ - 1
- ⅙ x = ⅚ - 6/6
- ⅙ x = - ⅙ / × ( - 1 )
⅙ x = ⅙ / : ⅙
x = ⅙ : ⅙
x = ⅙ × 6
x = 6/6
x = 1.
b ) ( 2x - 3 ) / 4 = ½ + x
2x/4 - ¾ = ½ + x
2/4 x - ¾ = ½ + x
½ x - ¾ = ½ + x / - x + ¾
½ x - x = ½ + ¾
½ x - 2/2 x = ½ + ¾
-½ x = ½ + ¾
- ½ x = 2/4 + ¾
- ½ x = 5/4 / × ( - 1 )
½ x = - 5/4 / : ½
x = - 5/4 : ½
x = - 5/4 × 2
x = ( - 5 × 2 ) / 4
x = - 10/4
x = - 5/2
x = - 2 ½
x = - 2,5.
c ) ( x + 2 ) / 9 + ( x - 1 ) / 3 = 1
x/9 + 2/9 + x/3 - ⅓ = 1
1/9 x + 2/9 + ⅓ x - ⅓ = 1 / - 2/9 + ⅓
1/9 x + ⅓ x = 1 - 2/9 + ⅓
1/9 x + 3/9 x = 1 - 2/9 + ⅓
4/9 x = 1 - 2/9 + ⅓
4/9 x = 9/9 - 2/9 + 3/9
4/9 x = 7/9 + 3/9
4/9 x = 10/9 / : 4/9
x = 10/9 : 4/9
x = 10/9 × 9/4
x = ( 10 × 9 ) / ( 9 × 4 )
x = 90/36
x = 45/18
x = 15/6
x = 5/2
x = 2 ½
x = 2,5.
d ) ( 2x + 3 ) / 5 = ( 2 - x ) / 3 + x
2x/5 + ⅗ = ⅔ - x/3 + x
⅖ x + ⅗ = ⅔ - ⅓ x + x / + ⅓ x - x - ⅗
⅖ x + ⅓ x - x = ⅔ - ⅗
6/15 x + 5/15 x - x = ⅔ - ⅗
11/15 x - x = ⅔ - ⅗
11/15 x - 15/15 x = ⅔ - ⅗
-4/15 x = ⅔ - ⅗
- 4/15 x = 10/15 - 9/15
- 4/15 x = 1/15 / × ( - 1 )
4/15 x = - 1/15 / : 4/15
x = - 1/15 : 4/15
x = - 1/15 × 15/4
x = ( - 1 × 15 ) / ( 15 × 4 )
x = - 15/60
x = - 5/20
x = - ¼
x = - 0,25.
e ) ( 3x - 5 ) / 2 - ( 5x - 1 ) / 10 = 0
3x/2 - 5/2 - ( 5x/10 - 1/10 ) = 0
3x/2 - 5/2 - 5x/10 - ( - 1/10 ) = 0
3x/2 - 5/2 - 5x/10 + 1/10 = 0
3/2 x - 5/2 - 5/10 x + 1/10 = 0
3/2 x - 5/2 - ½ x + 1/10 = 0 / + 5/2 - 1/10
3/2 x - ½ x = 5/2 - 1/10
3/2 x - ½ x = 25/10 - 1/10
3/2 x - ½ x = 24/10
3/2 x - ½ x = 12/5
2/2 x = 12/5
x = 12/5
x = 2 ⅖
x = 2,4.
f ) x/2 = ⅖ ( 4 - x ) - 4
x/2 = ⅖ × 4 - ⅖ x - 4
x/2 = 8/5 - ⅖ x - 4
½ x = 8/5 - ⅖ x - 4 / + ⅖ x
½ x + ⅖ x = 8/5 - 4
5/10 x + 4/10 x = 8/5 - 4
9/10 x = 8/5 - 4
9/10 x = 8/5 - 20/5
9/10 x = - 12/5 / : 9/10
x = - 12/5 : 9/10
x = - 12/5 × 10/9
x = ( - 12 × 10 ) / ( 5 × 9 )
x = - 120/45
x = - 40/15
x = - 8/3
x = - 2 ⅔.
g ) ( 2x - 1 ) / 5 - ( x - 2 ) / 2 = 0,7 x
2x/5 - ⅕ - ( x/2 - 2/2 ) = 0,7 x
2x/5 - ⅕ - x/2 - ( - 2/2 ) = 0,7 x
2x/5 - ⅕ - x/2 + 2/2 = 0,7 x
2x/5 - ⅕ - x/2 + 2/2 = 7/10 x
⅖ x - ⅕ - ½ x + 2/2 = 7/10 x
⅖ x - ⅕ - ½ x + 1 = 7/10 x / - 7/10 x + ⅕ - 1
⅖ x - ½ x - 7/10 x = ⅕ - 1
4/10 x - 5/10 x - 7/10 x = ⅕ - 1
-1/10 x - 7/10 x = ⅕ - 1
- 8/10 x = ⅕ - 1
- ⅘ x = ⅕ - 1
- ⅘ x = ⅕ - 5/5
- ⅘ x = - ⅘ / × ( - 1 )
⅘ x = ⅘ / : ⅘
x = ⅘ : ⅘
x = ⅘ × 5/4
x = ( 4 × 5 ) / ( 5 × 4 )
x = 20/20
x = 10/10
x = 5/5
x = 1.
h ) 2x - ( 3x + 5 ) / 4 = - ¼ x - 1
2x - ( 3x/4 + 5/4 ) = - ¼ x - 1
2x - 3x/4 - 5/4 = - ¼ x - 1
2x - ¾ x - 5/4 = - ¼ x - 1 / + ¼ x + 5/4
2x - ¾ x + ¼ x = - 1 + 5/4
2x - 2/4 x = - 1 + 5/4
2x - ½ x = - 1 + 5/4
4/2 x - ½ x = - 1 + 5/4
3/2 x = - 1 + 5/4
3/2 x = - 4/4 + 5/4
3/2 x = ¼ / : 3/2
x = ¼ : 3/2
x = ¼ × ⅔
x = ( 1 × 2 ) / ( 4 × 3 )
x = 2/12
x = ⅙.
