Question

Cual es la justificación de este paso

`(3)/(2)[6(x-3+2]=-6`

Answer 1

3
2
(
6
(
x
−
3
+
2
)
)
=
−
6
Step 1: Simplify both sides of the equation.
3
2
(
6
(
x
−
3
+
2
)
)
=
−
6
9
x
+
−
9
=
−
6
(Distribute)
9
x
−
9
=
−
6
Step 2: Add 9 to both sides.
9
x
−
9
+
9
=
−
6
+
9
9
x
=
3
Step 3: Divide both sides by 9.
9
x
9
=
3
9
x
=
1
3

Answer 2

x = 1/5

Explanation:

Expand the following:

(3×5 (x - 3 + 2))/2 = -6

Add like terms. 2 - 3 = -1:

(5×3 (x - 1))/2 = -6

5×3 = 15:

(15 (x - 1))/2 = -6

15 (x - 1) = 15 x - 15:

(15 x - 15)/2 = -6

(15 x - 15)/2 = (15 x)/2 + 1/2 (-15):

(15 x)/2 - 15/2 = -6

Add 15/2 to both sides:

(15 x)/2 + (15/2 - 15/2) = 15/2 - 6

15/2 - 15/2 = 0:

(15 x)/2 = 15/2 - 6

15/2 - 6 = 3/2:

(15 x)/2 = 3/2

Multiply both sides of (15 x)/2 = 3/2 by 2/15:

(2×15 x)/(15×2) = 2/15×3/2

2/15×1/2×15 = (2×15)/(15×2):

(2×15)/(15×2) x = 2/15×3/2

2/15×3/2 = (2×3)/(15×2):

(2×15 x)/(15×2) = (2×3)/(15×2)

(2×15 x)/(15×2) = (15×2)/(15×2)×x = x:

x = (2×3)/(15×2)

(2×3)/(15×2) = 2/2×3/15 = 3/15:

x = 3/15

The gcd of 3 and 15 is 3, so 3/15 = (3×1)/(3×5) = 3/3×1/5 = 1/5:

Answer: x = 1/5