[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
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20a <_
-15 subtract
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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
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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
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-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
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4x + 6 <
4 add
-6 -6
subtract 6 from each side
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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
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2y + 14 < 8 subtract
-14
-14 subtract 14 from
each side
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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
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k - 15 >_ 1
subtract
+15 +15 add 15 to each side
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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
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5r >_ -4 + 4r add
-4r -4r subtract 4r from each side
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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
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z
+ 7 >_ 4 add
-7 -7 subtract 7 from each side
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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
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-2 + 6d <
6 add
+ 2 +2 add 2 to each side
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6d < 8 add
___ ___
6
6 divide each side by 6
d < 4/3 reduce and cancel
result: d < 4/3