What is the reason for each step in the solution of the inequality? 28−3(x−2)< 5x+10

division property of order

subtraction property of order

addition property of order

distributive property

combine like terms

given

1.

28−3(x−2)< 5x+10

2.

28−3x+6< 5x+10

3.

34−3x< 5x+10

4.

34< 8x+10

5.

24< 8x

6.

3

1. 28 − 3(x − 2) < 5x + 10            Given

2. 28 − (3)(x) + (-3)(-2) < 5x + 10       Distributive Property a(b + c) = ab+ ac

28 − 3x + 6 < 5x + 10

3.  (28 + 6) - 3x < 5x + 10             Combine Like Terms

34 − 3x < 5x + 10

4. 34 - 3x + 3x < 5x + 3x + 10             Addition Property of Order

34 < 8x + 10

5. 34 - 10 < 8x + 10 - 10        Subtraction Property of Order

24 < 8x

6. 24/8 < 8x/8        Division Property of Order

3 < x

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: