[solving inequalities part 1][section 16]

(1.) 3n - 2(n - 1) >_ 0 here is the problem

3n - 2n + 2 >_ 0 multiply thru parentheses

n + 2 >_ 0 combine like terms

-2 -2 subtract 2 from each side
______________
n >_ -2 subtract

result: n >_ -2

Here is the graph:

(2.) 4t - 3(t + 6) > -5 here is the problem

4t - 3t - 18 > -5 multiply thru parentheses

t - 18 > -5 combine like terms

+ 18 +18 add 18 to each side
________________
t > 13 add

result: t > 13

Here is the graph:

(3.) 3(2z - 1) + 8 < 5z here is the problem

6z - 3 + 8 < 5z multiply thru parentheses

6z + 5 < 5z combine like terms

-5 - 5 subtract 5 from each side
________________
6z < 5z - 5 subtract

-5z -5z subtract 5z from each side
_______________________
z < -5 subtract

result: z < -5

Here is the graph:

(4.) 0 <_ 4(1 - 7n) + 29n here is the problem

0 <_ 4 - 28n + 29n multiply thru parentheses

0 <_ 4 + n combine like terms

-4 -4 subtract 4 from each side
_______________
-4 <_ n subtractS

result: n >_ -4

Here is the graph:

(5.) 5q + 2(9 - 2q) <_ 0 here is the problem

5q + 18 - 4q <_ 0 multiply thru parentheses

q + 18 <_ 0 combine like terms

-18 -18 subtract 18 from each side
__________________
q <_ -18 subtract

result: q <_ -18

Here is the graph:

(6.) -5(1 - 5x) > -12(1 - 2x) here is the problem

-5 + 25x > -12 + 24x multiply thru parentheses

-24x -24x subtract 24x from each side
_________________________
-5 + x > -12 subtract

+ 5 + 5 add 5 to each side
______________________
x > -7 add

result: x > -7

Here is the graph:

(7.) 9x + 1 <_ 4(2x + 3) here is the problem

9x + 1 <_ 8x + 12 multiply thru parentheses

-1 -1 subtract 1 from each side
_______________________
9x <_ 8x + 11 subtract

-8x -8x subtract 8x from each side
_________________________

x <_ 11 subtract

result: x <_ 11

Here is the graph:



(8.) 7 + 4(2y) <_ 7y - 5 here is the problem

7 + 8y <_ 7y - 5 multiply

-7 -7 subtract 7 from each side
________________________
8y <_ 7y - 12 subtract

- 7y -7y subtract 7y from each side
_______________________

y <_ -12 subtract

result: y <_ -12

Here is the graph:

(9.) 1 + 2(y - 1) >_ 3y

1 + 2y - 2 >_ 3y multiply thru parentheses

2y - 1 >_ 3y combine like terms

-2y -2y subtract 2y from each side
_____________________
-1 >_ y subtract

result: y <_ -1

Here is the graph:

(10.) 6x + 2 >_ 14 + 5x here is the problem

-5x -5x subtract 5x from each side
________________________
x + 2 >_ 14 subtract

-2 -2 subtract 2 from each side
___________________
x >_ 12 subtract

result: x >_ 12

Here is the graph: