Find the solution set for the equation.
|3m + 4| + 6 = 12
two ways
1.
(3m+4) = 6
2.
-(3m+4) = 6
|3m + 4| + 6 = 12,
|3m + 4| = 6,
3m + 4 = +-6,
m = (-4 + (+-6))/3 = 2/3, and -10/3.
To find the solution set for the equation, we need to isolate the absolute value term and solve for the variable.
Let's start by subtracting 6 from both sides of the equation:
|3m + 4| = 12 - 6
|3m + 4| = 6
Now, we have an absolute value equation. To solve it, we'll consider two cases:
Case 1: 3m + 4 is positive:
In this case, we can remove the absolute value signs, so we have:
3m + 4 = 6
Now, subtract 4 from both sides:
3m = 6 - 4
3m = 2
Divide both sides by 3:
m = 2/3
Case 2: 3m + 4 is negative:
In this case, the absolute value equation becomes:
-(3m + 4) = 6
Now, we need to distribute the negative sign to the terms inside the parentheses:
-3m - 4 = 6
Add 4 to both sides:
-3m = 6 + 4
-3m = 10
Divide both sides by -3:
m = 10/-3
So, the solution set for the equation is:
m = 2/3, m = 10/-3