172k views
4 votes
7Iy-9I+3>38
7 |y - 9| + 3 \geqslant 38solve for y

User Thijs D
by
6.4k points

1 Answer

5 votes

To find the solution for this inequality, we can proceed as follows:


7\cdot|y-9|+3>38\Rightarrow7\cdot|y-9|>38-3\Rightarrow7\cdot|y-9|>35\Rightarrow|y-9|>(35)/(7)

Then, we have:


|y-9|>5

Then, because we have the function absolute value, we have to solve the next two inequalities:


y-9>5,y-9<-5

Therefore, solving for these two inequalities, we have:


y-9>5\Rightarrow y>5+9\Rightarrow y>14_{}

And


y-9<-5\Rightarrow y<-5+9\Rightarrow y<4

Then, the two solutions are y > 14 and y < 4 or the solutions are in the interval form:

(14, infinity) and (-infinity, 4). Graphically:

7Iy-9I+3>38 7 |y - 9| + 3 \geqslant 38solve for y-example-1
User Ziofil
by
6.6k points