Answer:
1- The solution of I2x + 5I = 9 is {-7 , 2}
2- The solution of I2x + 7I + 2 = 11 is {-8 , 1}
3- The solution of I5 - xI = 6 is {-1 , 11}
4- The solution of I6x - 8I + 7 = 5 is ∅
5- The solution of Ix + 3I = 12 is {-15 , 9}
6- The solution of Ix - 3I = -12 is ∅
Step-by-step explanation:
* At first lets explain the meaning of IxI = a
- If IxI = a ⇒ then x = a or x = -a
- IxI never give a negative answer, because IxI means the
magnitude of x is always positive
Ex: I-2I is 2
* Now lets find the solution of each equation
1- ∵ I2x + 5I = 9
∴ 2x + 5 = 9 ⇒ subtract 5 from both sides
∴ 2x = 4 ⇒ divide both sides by 2
∴ x = 2
OR
∴ 2x + 5 = -9 ⇒ subtract 5 from both sides
∴ 2x = -14 ⇒ divide both sides by 2
∴ x = -7
* The solution of I2x + 5I = 9 is {-7 , 2}
2- ∵ I2x + 7I + 2 = 11 ⇒ Subtract 2 from both sides
∴ I2x + 7I = 9
∴ 2x + 7 = 9 ⇒ subtract 7 from both sides
∴ 2x = 2 ⇒ divide both sides by 2
∴ x = 1
OR
∴ 2x + 7 = -9 ⇒ subtract 7 from both sides
∴ 2x = -16 ⇒ divide both sides by 2
∴ x = -8
* The solution of I2x + 7I + 2 = 11 is {-8 , 1}
3- ∵ I5 - xI = 6
∴ 5 -x = 6 ⇒ subtract 5 from both sides
∴ -x = 1 ⇒ divide both sides by -1
∴ x = -1
OR
∴ 5 -x = -6 ⇒ subtract 5 from both sides
∴ -x = -11 ⇒ divide both sides by -1
∴ x = 11
* The solution of I5 - xI = 6 is {-1 , 11}
4- ∵ I6x - 8I + 7 = 5 ⇒ Subtract 7 from both sides
∴ I6x - 8I = -2
- I I never give negative answer
* The solution of I6x - 8I + 7 = 5 is ∅
5- ∵ Ix + 3I = 12
∴ x + 3 = 12 ⇒ subtract 3 from both sides
∴ x = 9
OR
∴ x + 3 = -12 ⇒ subtract 3 from both sides
∴ x = -15
* The solution of Ix + 3I = 12 is {-15 , 9}
6- ∵ Ix - 3I = -12
- I I never give negative answer
* The solution of Ix - 3I = -12 is ∅
942 units³ ---Second choice