2007-08-14 07:19:43 · 15 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
|2x + 3| = 17
so either
2x + 3 = 17
2x = 14
x = 7
or
2x + 3 = -17
2x = -20
x = -10
The two solutions are 7, -10.
2007-08-14 07:25:36 · answer #1 · answered by Anonymous · 3⤊ 1⤋
|2x + 3| - 6 = 11 // add 6
|2x + 3| = 17
Now, split into two cases:
1. 2x + 3 >= 0 -> x >= - 1.5
In this case |2x + 3| = 2x + 3
2x + 3 = 17
2x = 14
x=7 > -1.5
Checking the solution:
|2*7 + 3| - 6 = |14 + 3| - 6 = |17|-6 = 17-6 = 11 This is one solution.
2. 2x + 3 < 0 -> x < -1.5
-(2x + 3) = 17
-2x - 3 = 17 // add 3
-2x = 20 // divide by -2
x = -10 < -1.5
Checking the solution:
|2x + 3| - 6 = |2*(-10) + 3| - 6 = |-20 + 3| - 6 = |-17| - 6 =
= 17 - 6 = 11.
This is another solution.
2007-08-14 07:31:20 · answer #2 · answered by Amit Y 5 · 1⤊ 0⤋
Get the absolute value by itself.
|2x + 3| = 17
Since the answer to an absolute value problem is always positive, you have to take into account that what is inside COULD be negative. So, you split the absolute value apart and solve to obtain two possible values for the variable.
2x + 3 = 17
2x = 14
x = 7
-(2x + 3) = 17
-2x - 3 = 17
-2x = 20
x = -10
The answers are -10 and 7.
2007-08-14 07:29:43 · answer #3 · answered by its_victoria08 6 · 1⤊ 0⤋
l 2x + 3 l - 6 = 11
l 2x + 3 l can equal two different values:
l 2x + 3 l = l 2x + 3 l or l -2x - 3 l
You can plug these two values in, without the absolute value sign into the equation, and find two values of x:
2x + 3 - 6 = 11
Subtract 6 from 3:
2x - 3 = 11
Add 3 to both sides:
2x = 14
Divide by 2 on both sides to solve for x:
x = 7
This is one possible value for x.
To find the other value, plug in -2x - 3 and find x:
-2x - 3 - 6 = 11
Subtract 6 from - 3:
-2x - 9 = 11
Add 9 to both sides:
-2x = 20
Finally, divide by -2 to find x:
x = -10
These are your two answer: x = 7, or x = - 10.
Hope this helps!
2007-08-14 07:34:41 · answer #4 · answered by zero_max12 2 · 0⤊ 0⤋
Multiply each and every thing by utilising 6 to cancel off the - a million/6 (-a million/6 will become -a million and a million/3 will become 2): 2(2x-5) = -(11-9x) enhance the brackets by utilising multiplying the words exterior the brackets to the left (2 and -a million) by utilising each and all of the words interior the brackets: 4x - 10 = -11 + 9x upload 10 to the two aspects: 4x = -a million + 9x Subtract 9x from the two aspects: -5x = -a million Divide the two aspects by utilising -5: x = a million/5
2016-11-12 07:52:54 · answer #5 · answered by Anonymous · 0⤊ 0⤋
|2x+3| - 6 =11
|2x+3| = 17
2x+3 = +/- 17
2x = -3 + 17 and 2x = -3 - 17
2x = 14 and 2x = -20
x = 7 and x = -10
2007-08-14 07:26:22 · answer #6 · answered by Jasmine 2 · 3⤊ 0⤋
(2x +3) - 6 = 11 or -(2x +3) - 6 = 11
2x + 3 - 6 = 11 -2x - 3 - 6 = 11
2x = 14 -2x = 20
x = 7 or x = -10
2007-08-14 07:27:11 · answer #7 · answered by Larry C 3 · 2⤊ 1⤋
|2x + 3| - 6 = 11
11+6=17
2x+3=17
x=7
(2x7+3)-6=11
2007-08-14 07:31:14 · answer #8 · answered by dude 2 · 0⤊ 1⤋
|2x + 3| - 6 = 11
|2x + 3| = 17
|2x + 3|^2 = 17^2
4x^2+12x+9-289=0
4x^2+12x-280=0 --> /4
x^2+3x-70=0
X1;X2= (-3 +- (9-4*(-70))^(1/2)) / 2
=( -3+-17)/2
X1 = (-3+17)/2 = 7
X2 = (-3 -17)/2 = -10
2007-08-14 07:32:42 · answer #9 · answered by Nahuel J 2 · 0⤊ 0⤋
|2x+3|-6=11
2x+3=17
2x=14
x=7
2007-08-14 07:42:29 · answer #10 · answered by Anonymous · 0⤊ 0⤋