This is absolutely true! Anything that is constant because of consistency, regularity, and repetition is a pattern.
[x-1]=5x+10
We have two equations:
1) x-1=5x+10
x-1=5x+10
x-5x=10+1
-4x=11
x=-11/4
2) x-1=-(5x+10)
x-1=-(5x+10)
x-1=-5x-10
x+5x=-10+1
6x=-9
x=-9/6=-3/2
we have two possible solutions:
solution₁; x=-11/4
solution₂: x=-3/2
we check it out:
1) x=-11/4
[x-1]=5x+10
[-11/4 - 1]=5(-11/4)+10
[(-11-4)/4]=-55/4 + 10
[-15/4]=(-55+40) /4
15/4≠-15/4 This solution don´t work.
2) x=-3/2
[x-1]=5x+10
[-3/2 - 1]=5(-3/2)+10
[(-3-2)/2]=-15/2 + 10
[-5/2]=(-15+20)/2
5/2=5/2; this solution works.
Therefore:
Answer: x=-3/2.
The 3 consecutive numbers are 88, 89, and 90. So 90 is the answer.
Why not start out by writing a linear relationship for the plant height?
h(m) = 10 + 3m, where h is the height in mm and m is the time in years, starting from zero (0).
After 8 months, the plant height is h(8) = 10 mm + 3(8) mm, or 34 mm.
After 3 years (36 months), the plant ht. is h(36) = 118 mm.
