Solve |y - 2|< 10

a.) {y|-8 < y < 12}
b.) {y|-12 < y < 8}
c.) {y|-8 < y < 8}

OPTION A

Step-by-step explanation:

We have:

Adding 'a' to the components:

- b + a < x < b + a

This is the result.

Here, we have: |y - 2| < 10

⇒ -10 < y - 2 < 10

Adding 2, we get:

- 10 + 2 < y < 10 + 2

⇒ - 8 < y < 12

That is, 'y' can take any value between -8 and 12.

In set notation: {y : - 8 < y < 12} : OPTION A is the answer.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.