|2x - 37| = 15
2006-07-13 12:20:27 · 12 answers · asked by No One! 2 in Science & Mathematics ➔ Mathematics
|2x - 37| = 15
2x - 37 = ±15
2x = 37 ± 15
x = (37 ± 15) / 2.
x = (37 + 15) / 2 = 52 / 2 = 26, or
x = (37 - 15) / 2 = 22 / 2 = 11.
Checking...
|2(26) - 37| = |52 - 37| = 15, or
|2(11) - 37| = |22 - 37| = |-15| = 15.
x = 26 or x = 11.
[Edited to comment]
Too many people attempting to solve this problem are forgetting what an absolute value is. In one variable, it represents the distance from zero on a number line.
In this problem, there are two points with a distance of 15 from zero... they're 15 or -15. This forces the problem to become a compound equation:
2x - 37 = 15 or 2x - 37 = -15. You have to solve them both!
[Edited to comment again]
Thanks, fizixx!
2006-07-13 12:25:19 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Absolute value equations are very important in algebra and calculus.
In general, without restrictions on x, \sqrt{x^2}=|x|; |x|=x if x \geq 0 and -x if x < 0.
So, solving |2x-37|=15 means solving 2x-37=15 and 2x-37=-15.
Solving these two equations gives us:
2x-37=15 -> 2x=52 -> x=26
and
2x-37=-15->2x=22 -> x=11.
So, the absolute value equation has the two solutions: x=26 and x=11.
To see this with your graphics calculator, graph y=|2x-37| and y=15. Use [0,40] for your x-window and [0,30] for your y-window. That should give you a decent picture.
2006-07-13 19:43:03 · answer #2 · answered by Anonymous · 0⤊ 0⤋
|2x - 37| = 15
Find your like terms and put them together (37 & 15)
2x-(37+37)=15+37 - you must cancel the 37 out by adding it to 15 - that's the rule.
15+37=52
2x=52
now you are solving for x - (what times 2 equals 52)
2x26=52
x=26
2006-07-13 19:34:54 · answer #3 · answered by femmenoire@sbcglobal.net 4 · 0⤊ 0⤋
(2x -37) = 15
(2x -37)+ 37 = 15 +37
2x = 15 + 37
2x = 52
(2x) / 2 = 52 / 2
x = 52 / 2
x = 26
2006-07-13 19:25:33 · answer #4 · answered by Picture Taker 7 · 0⤊ 0⤋
2x-37+37=15+37
2x=52
x=26
2006-07-13 19:23:53 · answer #5 · answered by dhills23 3 · 0⤊ 0⤋
x=26
2006-07-13 19:23:56 · answer #6 · answered by trumpets_rock88005 2 · 0⤊ 0⤋
|2x - 37| = 15
2x - 37 = 15 or -15
2x = 52 or 22
x = 26 or 11
ANS : 11 or 26
2006-07-14 09:35:41 · answer #7 · answered by Sherman81 6 · 0⤊ 0⤋
It's really easy, I know you can do it!
2x = 15 + 37
2x = 52
x = 26
2006-07-13 19:24:19 · answer #8 · answered by Psyl*Girl 2 · 0⤊ 0⤋
Louise hits it on the head.
She's using the fact that in absolute values:
|x| = x is x is >= 0 -or-
|x| = x is -x if x <= 0
And what she did was apply that to your problem. She gets the 10 man.
2006-07-13 19:40:10 · answer #9 · answered by Anonymous · 0⤊ 0⤋
26 or 11 i think
2006-07-13 19:25:51 · answer #10 · answered by Anonymous · 0⤊ 0⤋