Solve the equation. 11 = |m + 5| Select the correct choice and, if necessary, fill in the answer box in your choice below.
OA. m = (Simplify your answer. Use a comma to separate answers as needed.)
OB. There is no solution.
To solve the equation 11 = |m + 5|, we need to consider two cases: one where the expression inside the absolute value is positive, and one where it is negative.
Case 1: m + 5 is positive (m + 5 > 0)
In this case, the absolute value can be removed. Therefore, m + 5 = 11.
Solving this equation, we get m = 6.
Case 2: m + 5 is negative (m + 5 < 0)
In this case, the expression inside the absolute value sign needs to be negated. Therefore, m + 5 = -11.
Solving this equation, we get m = -16.
Therefore, the solutions to the equation 11 = |m + 5| are m = 6 and m = -16.
OA. m = 6, -16
To solve the equation 11 = |m + 5|, we can break it down into two cases and solve for m in each case.
Case 1: m + 5 is positive.
In this case, the equation becomes 11 = m + 5. To solve for m, we subtract 5 from both sides:
11 - 5 = m + 5 - 5
6 = m
Case 2: m + 5 is negative.
In this case, the equation becomes 11 = -(m + 5). To solve for m, we multiply both sides by -1 and distribute the negative sign:
11 = -1 * (m + 5)
11 = -m - 5
To isolate m, we add 5 to both sides:
11 + 5 = -m - 5 + 5
16 = -m
Finally, we multiply both sides by -1 to solve for m:
-1 * 16 = (-1) * -m
-16 = m
Therefore, the solutions to the equation are m = 6 and m = -16.
OA. m = 6 , -16
To solve the equation 11 = |m + 5|, we need to isolate the absolute value expression and consider both the positive and negative cases.
1. Start by removing the absolute value bars by considering two cases:
Case 1: (m + 5) is positive:
In this case, we can rewrite the equation as:
11 = m + 5
Case 2: (m + 5) is negative:
In this case, we need to negate the expression within the absolute value bars:
11 = -(m + 5)
To remove the negative sign, we rewrite the equation as:
11 = -m - 5
2. Solve each equation separately:
Case 1: m + 5 = 11
Subtract 5 from both sides:
m = 11 - 5
m = 6
Case 2: -m - 5 = 11
Add 5 to both sides:
-m = 11 + 5
-m = 16
Multiply both sides by -1 to isolate m:
m = -16
3. Final answers:
The solutions to the equation 11 = |m + 5| are m = 6 and m = -16.
Thus, the correct choice is:
OA. m = 6, -16