How to solve 18 + x = (48 + x) * 4 / 9

How to solve 18 + x = (48 + x) * 4 / 9

18+x＝（48+x）* 4/9
18+x=48*4/9+4/9x
x-4/9x=192/9-18
5/9x=192/9-18
5x=192-162
5x=30
x=6

If the equation 9 ^ (- |x-2 |) - 4 * 3 ^ (- |x-2 |) + a = 0 has a solution, find the value range of A

Let t = 3 ^ (- |x-2 |), then the original equation is reduced to T & sup2; - 4T + a = 0
∵－|x-2|≤0
∴0＜3^(-|x-2|)≤1
So the original equation has a solution, which is equivalent to the above equation having a solution on (0,1]
a=-t²＋4t＝－(t²-4t）＝－（t-2）²＋4
Since the axis of symmetry is t = 2, the interval is (0,1]
So it increases monotonically in this interval
∴0＜a≤3