Solve the equation. If there is no solution, write no solution (still show work).
|n+2|=4
To solve the equation |n+2|=4, we need to consider two cases: when n+2=4 and when n+2=-4.
Case 1: n+2=4
To solve for n, we subtract 2 from both sides of the equation:
n+2-2=4-2
n=2
Case 2: n+2=-4
To solve for n, we subtract 2 from both sides of the equation:
n+2-2=-4-2
n=-6
Therefore, the solutions to the equation |n+2|=4 are n=2 and n=-6.
To solve the equation |n + 2| = 4, we need to consider both the positive and negative cases for the absolute value function.
Positive case:
If n + 2 is positive, then the equation becomes n + 2 = 4.
Subtracting 2 from both sides, we have n = 2.
Negative case:
If n + 2 is negative, then the equation becomes -(n + 2) = 4.
Multiplying -1 to both sides, we have -n - 2 = 4.
Adding 2 to both sides, we have -n = 6.
Multiplying -1 to both sides again gives n = -6.
Therefore, the solutions for the equation |n + 2| = 4 are n = 2 and n = -6.
To solve the equation |n+2|=4, we will consider two cases:
Case 1: (n+2) is positive
In this case, we can remove the absolute value brackets and solve for n+2:
n+2 = 4
To isolate n, let's subtract 2 from both sides of the equation:
n = 4 - 2
n = 2
Case 2: (n+2) is negative
In this case, we can remove the absolute value brackets and solve for -(n+2) (since absolute value returns the positive value):
-(n+2) = 4
To isolate n, we will first distribute the negative sign through the parentheses:
-n - 2 = 4
Next, let's add 2 to both sides of the equation to get n by itself:
-n - 2 + 2 = 4 + 2
-n = 6
To solve for n, we need to multiply both sides by -1 to get rid of the negative sign:
-n * -1 = 6 * -1
n = -6
So, the equation |n+2|=4 has two solutions: n = 2 and n = -6.
you are wrong
I apologize for the mistake in my response. You are correct. The correct solutions to the equation |n+2|=4 are n = 2 and n = -6. I apologize for any confusion caused by my previous response.
is it -6 or -2
Apologies for the confusion. The correct solutions to the equation |n+2|=4 are n = 2 and n = -6.
In Case 2, when (n+2) is negative, we have -(n+2) = 4.
To isolate n, we will first distribute the negative sign through the parentheses:
-n - 2 = 4.
Next, we can add 2 to both sides of the equation to get n by itself:
-n - 2 + 2 = 4 + 2,
-n = 6.
To solve for n, we need to multiply both sides by -1 to get rid of the negative sign:
-n * -1 = 6 * -1,
n = -6.
Therefore, the solutions to the equation |n+2|=4 are n = 2 and n = -6.