Solve the inequality and graph the solution. -12+ 5(9p+3)-36p < 6p-12

Given inequality is,

-12 + 5(9p+3) - 36p < 6p - 12

By distributive property,

-12 + 45p + 15 - 36p < 6p - 12

Combine like terms,

3 + 9p < 6p - 12

Additive property of equality,

15 + 9p < 6p

Subtraction property of equality,

9p < 6p - 15

3p < -15

⇒ p < -5

That is, solution of the given inequality is (-∞, 5)

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.

77

step-by-step explanation: