[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
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-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
______________________
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
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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