Solve the following systems of linear in equations:
, x > 0
and
When,
Subtracting 3 from both the sides
Signs of 1 – 3x:
1 – 3x = 0 →
(Subtract 1 from both the sides and then divide both sides by -3)
1 – 3x > 0 →
(Subtract 1 from both the sides, then multiply by -1 on both sides and then divide both sides by 3)
1 – 3x < 0 →
(Subtract 1 from both the sides, then multiply by -1 on both sides and then divide both sides by 3)
Interval satisfying the required condition ≤ 0 , x > 0
or
Or
Now when,
Subtracting 3 from both the sides
Dividing both sides by 3
Multiplying by -1 on both sides
Signs of x - 1:
x – 1 = 0 → x = 1 (Adding 1 to both the sides)
x – 1 > 0 → x > 1 (Adding 1 to both the sides)
x – 1 < 0 → x < 1 (Adding 1 to both the sides)
Interval satisfying the required condition: ≤ 0
x ≤ 1
Combining the intervals:
such that x > 0