Tentukan nilai x yang memenuhi ketidaksamaan. |3x + 12| < 2 |x - 6|

Step-by-step explanation:

|3x + 12| < 2 |x - 6|

|3(x + 4)| < 2 |x - 6|        ⇒  -4 and 6 are "zeros"

1°.  x∈(-∞, -4> ⇒ |3x + 12| = - (3x + 12)  and  2|x - 6| = -2(x-6)

-(3x + 12) < -2(x - 6)

-3x - 12 < -2x + 12

  -x < 24

x > -24  ∧ x∈(-∞-4> ⇒ x∈(-18, -4>

2°.  x∈(-4, 6)  ⇒ |3x + 12| = 3x+12  and  2|x - 6| = -2(x-6)

3x + 12 < -2(x - 6)

3x + 12 < -2x + 12

  5x < 0

x < 0  ∧ x∈(-4, 6)  ⇒ x∈(-4, 0)

3°.  x∈(6, ∞)  ⇒ |3x + 12| = 3x+12  and  2|x - 6| = 2(x-6)

3x + 12 < 2(x - 6)

3x + 12 < 2x - 12

  x < -24

x < -24  ∧  x∈(6, ∞)  ⇒ x∈∅

x∈1°∪2°∪3°

x∈(-24, -4>∪(-4, 0)∪∅

x∈(-24, 0)   ⇒   -24 < x < 0

87%

step-by-step explanation:

apex answer

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3