Question

7Iy-9I+3>38 $7 |y - 9| + 3 \geqslant 38$solve for y

Answer 1

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

$7\cdot|y-9|+3>38\Rightarrow7\cdot|y-9|>38-3\Rightarrow7\cdot|y-9|>35\Rightarrow|y-9|>\frac{35}{7}$

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: