2007-02-04 06:43:07 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Multiply by 2 just to simplify things.
1/2 X + 3 < 2X - 6
becomes
X+6<4X-12
Set them equal to find where these two lines intersect.
X+6 = 4x - 12
18=3x
X=6
now check some values out for X.
When X = 6, 1/2X+3 becomes 6 and 2X-6 becomes 6...so this equation is not true for 6, but since they are both LINES, you can go up one and down one to see where it goes.
Check X=7.
6.5<8 TRUE!
Check X=5
5.5 < 4 FALSE!
So X must be > 6 for this equation to be TRUE.
2007-02-04 06:49:43 · answer #1 · answered by Brad L 4 · 0⤊ 0⤋
In about the same way one solves an equation; the only difference is that, when multiplying both sides by -1, the < turns to >, and vice-versa.
(1/2)x + 3 < 2x - 6
Multiplying both sides by 2, just to get rid of the fraction:
x + 6 < 4x - 12
x - 4x < -12 - 6
-3x < -18
3x > 18 (note how the inequality turned to the other side when multiplying by -1)
x > 6
In other words: all real numbers bigger than 6 are the solutions. This is expected, and common, when solving inequations (appear to be equations, but with < <= > >= instead of = ).
2007-02-04 15:22:11 · answer #2 · answered by jcastro 6 · 1⤊ 0⤋
whenever you get this kind of equation , be discriminative
your aim is to put what looks alike together
start with the numbers
1/2x + 3 < 2x - 6
now discriminate the numbers (by substracting 3 or adding 6 on both sides)
1/2x +3 + 6< 2x
1/2x + 9 < 2x
and then discriminate the numbers with the x by moving either to the other side
9 < 2x - 1/2x
9< (2-1/2)x
9 < 3/2x
And then find x by dividing both sides! (here divide by 3/2 or multiply by 3/2
9 * 3/2 < 3/2 * 2/3 * x
6
Got it?
2007-02-04 14:52:22 · answer #3 · answered by chocolateknight69 3 · 0⤊ 0⤋
Get all the x's on one side and all the numbers on the other side.
1/2x+3 < 2x-6
add 6 to both sides
1/2x+9 < 2x
subtract 1/2x from both sides
9 < 1.5x
divide both side by 1.5
6 < x
2007-02-04 14:48:38 · answer #4 · answered by Anonymous · 0⤊ 0⤋
subtract 2x to the other side
subtract 3 to the to right side
you should get -3/2x<-9
then divide by -3/2
-9/(-3/2)
x>6
2007-02-04 14:59:24 · answer #5 · answered by deadman 2 · 1⤊ 0⤋
Multiply both sides by 2:
x+6<4x-12
Subtract 4x from both sides:
-3x+6<-12
Subtract 6 from both sides:
-3x<-18
Divide -3 from both sides:
x>6
2007-02-04 15:33:31 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Put all x's on one side and constants on the other.
9 < 1.5x
x > 6
2007-02-04 14:47:19 · answer #7 · answered by gebobs 6 · 0⤊ 0⤋