[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
________________

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
______________________

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: