What is the value of x for the following equation: 26|2x+1|=52?
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We have to find x given that 26|2x+1|=52.
26|2x+1|=52
cancel 26 from both the sides.
=> |2x + 1| = 2
Now |x| represents the absolute value of x and has the same value for x as well as -x.
=> 2x + 1 = 2 and 2x + 1 = -2
=> 2x = 1 and 2x = -3
=> x = 1/2 and x = -3/2
Therefore we get x is equal to 1/2 and -3/2
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To find x if 26|2x+1| = 52.
Solution:
26|2x+1| = 52.
We divide both sides by 26:
|2x+1| = 2.
|2x+1|=2 implies 2x+1 = 2, or 2x+1 = -2 = 2.
If 2x+1 = 2, then 2x= 2 -1 = 1, so 2x/-2 = 1/2 . So x= -1/2.
If 2x+1 = -2, then 2x = -2-1 = -3. So 2x/2 = -3/2 = -3/2 = -3/2
Therefore if 26|2x+1| = 52, then x= 1/2 or x= -3/2.
For the beginning, we'll discuss the modulus.
Case 1:
l 2x + 1 l = 2x + 1 for 2x + 1 >= 0
2x >= -1
x >= -1/2
Now, we'll solve the equation:
26(2x + 1) = 52
We'll divide by 26:
2x + 1 = 2
We'll subtract 1 both sides, to isolate x to the left side:
2x = 2-1
We'll divide by 2:
x = 1/2
Since x =1/2 is in the interval of admissible values,[-1/2, +infinite], we'll accept it.
Case 2:
l 2x + 1l = -2x - 1 for 2x + 1 < 0
2x < -1
x < -1/2
Now, we'll solve the equation:
26(-2x - 1) = 52
-2x - 1 = 2
We'll add 1 both sides:
-2x = 3
x = -3/2
Since x = -3/2 belongs to the interval of admissible values, (-infinite, -1/2), we'll accept it, too.
The solutions of the given equation are: {-3/2 ; 1/2}.
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