The sum of three consecutive odd integers is more than 60 decreased by twice the smallest of the three integers. Let g = the greatest odd integer and write an inequality based on the given information.
Well I think it starts out like this but then I get confused when it says (Let g = the greatest odd integer)
x + (2+x) + (4+x) > 60 – 2x
2007-04-05 13:21:31 · 6 answers · asked by mike 1 in Science & Mathematics ➔ Mathematics
g-4 + g-2 + g > 60 - 2(g-4)
3g -6 > 68 - 2g
5g > 74
g>= 15
2007-04-05 13:26:44 · answer #1 · answered by hustolemyname 6 · 0⤊ 0⤋
Let: g = largest odd integer
g - 2 = next odd integer
g - 4 = smallest odd integer
The inequality will be:
g + (g - 2) + (g - 4) > 60 - 2(g-4) --> simplify by combining like terms
3g - 6 > 60 - 2g + 8 --> put all g's on left and all integers on right
5g > 74 --> final inequality
2007-04-05 20:36:41 · answer #2 · answered by jeffdeg 2 · 0⤊ 0⤋
In your equation, you used "x", which is the smallest of the three integers.
If you want to use "g", then you only need to substitute your "x" with "g-4". Because:
g = x + 4
So your equation becomes:
g + (g -2) + (g -4) > 60 - 2(g - 4)
3g - 6 > 68 - 2g
5g > 74
g > 74/5
Since g need to be an integer, g is equal to 15.
2007-04-05 20:30:25 · answer #3 · answered by Ben 3 · 0⤊ 0⤋
Just keep rolling along. You can add and subtract across an inequality, so just collect terms:
3x+6 >60-2x
5x > 54
The first odd number that meets this criteria is 11. The sum of 11,13 and 15 is 39, which is greater than 60-2(11) or 38
2007-04-05 20:27:59 · answer #4 · answered by cattbarf 7 · 0⤊ 0⤋
If g is the greatest, then the integers are g, g - 2, and g - 4.
2007-04-05 20:24:38 · answer #5 · answered by richardwptljc 6 · 0⤊ 0⤋
x+(2+x)+(4+x)>60-2x
x+2+x+4+x>60-2x
x+x+x+2x>60-2-4
5x>54
x>54/5
x>10,8
2007-04-05 20:27:09 · answer #6 · answered by Anonymous · 0⤊ 0⤋