[solving inequalities part 2][section 17]

(1.)   4(5a + 7) <_ 13            here is the problem

20a + 28 <_ 13       multiply thru parentheses

-28   -28       subtract 28 from each side
__________________
20a     <_  -15         subtract
____        ____
20           20        divide each side by 20

a <_ -3/4           reduce and cancel

result:  a <_ -3/4

(2.)    8z - 2(2z + 3) > 0             here is the problem

8z - 4z - 6 > 0         multiply thru parentheses

4z - 6 > 0          combine like terms

+  6  +6       add 6 to each side
_________________
4z      > 6        add
___     _____
4          4         divide each side by 4

z > 1.5          divide and cancel

result:   z > 1.5

(3.)   -2y - 5 >_ 10               here is the problem

+5   +5        add 5 to each side
__________________
-2y    >_ 15          add
____      ____
-2        -2         divide each side by -2

y <_ -7.5   divide, cancel, switch sign
result:  y <_ -7.5

(4.)   3(x + 2) < -x + 4        here is the problem

3x + 6 < -x + 4       multiply thru parentheses

+  x       +x         add x to each side
_____________________
4x + 6  <     4         add

-6       -6        subtract 6 from each side
______________________
4x     <   -2          subtract
____        ___
4          4       divide each side by 4

x < -1/2        reduce and cancel

result:  x < -1/2

(5.)   3(y + 2) + 8 < 10 - (2 - y)       here is the problem

3y + 6 + 8 < 10 - 2 + y    multiply thru parentheses

3y + 14 < 8 + y         combine like terms

-y             -y        subtract y from each side
____________________
2y + 14  < 8             subtract

-14    -14            subtract 14 from each side
____________________
2y         < -6            subtract
___           ___
2             2     divide each side by 2

y < -3            divide and cancel

result:  y < -3

(6.)  15x - 2(x - 4) > 3            here is the problem

15x - 2x + 8 > 3           multiply thru parentheses

13x + 8 > 3              combine like terms

-  8  -8        subtract 8 from each side
_______________
13x     > -5            subtract
___     ____
13       13        divide each side by 13

x > -5/13           cancel

result:  x > -5/13

(7.)  3(k - 4) - 3 >_ 2k + 1          here is the problem

3k - 12 - 3 >_ 2k + 1    multiply thru parentheses

3k - 15 >_ 2k + 1     combine like terms

-2k        -2k       subtract 2k from each side
__________________________
k - 15 >_      1        subtract

+15       +15         add 15 to each side
________________________
k        >_    16          add

result:  k >_ 16

(8.)  4 - 5(r - 2) <_ -2(-9 + 2r)        here is the problem

4 - 5r + 10 <_ 18 - 4r    multiply thru parentheses

-5r + 14 <_ 18 - 4r          combine like terms

5r - 14 >_ -18 + 4r   multiply thru by -1, switch sign

+14   + 14         add 14 to each side
____________________________
5r     >_ -4 + 4r          add

-4r              -4r   subtract 4r from each side
___________________________
r   >_  -4                  subtract

result:  r >_ -4

(9.)  3z + 7 >_ 8z - 2(5z - 2)       here is the problem

3z + 7 >_ 8z - 10z + 4    multiply thru parentheses

3z + 7 >_ -2z + 4         combine like terms

+ 2z      + 2z           add 2z to each side
_________________________
z  + 7 >_       4          add

-7          -7       subtract 7 from each side
_________________________
z        >_       -3      subtrac

result:   z >_ -3

(10.)  1 - (4d - 1) > 2(d - 3)       here is the problem

1 - 4d + 1 > 2d - 6    multiply thru parentheses

2 - 4d > 2d - 6      combine like terms

-2 + 4d < -2d + 6   multiply thru by -1, switch sign

+ 2d   +2d           add 2d to each side
________________________
-2  + 6d <     6           add

+ 2            +2           add 2 to each side
___________________________
6d < 8                    add
___  ___
6    6            divide each side by 6

d < 4/3         reduce and cancel

result:  d < 4/3