if 3abs(x+4)=8, then x=?
A. {-10,2}
B. {-2,2}
C. {-19,11}
D. {-22,-14}
which one? idek
To find the value of x in the equation 3abs(x+4)=8, we need to follow these steps:
Step 1: Remove the absolute value. To do this, we can divide both sides of the equation by 3: abs(x+4) = 8/3.
Step 2: Write two separate equations, one for the positive value and one for the negative value. When we remove the absolute value, we get two possible scenarios:
For the positive value: x + 4 = 8/3
For the negative value: -(x + 4) = 8/3
Step 3: Solve each equation separately:
For the positive value: x + 4 = 8/3
Subtract 4 from both sides: x = 8/3 - 4
Simplify: x = -4/3
For the negative value: -(x + 4) = 8/3
Distribute the negative sign: -x - 4 = 8/3
Add 4 to both sides: -x = 8/3 + 4
Simplify: -x = 24/3 + 8/3
Simplify further: -x = 32/3
Multiply both sides by -1 to isolate x: x = -32/3
Therefore, the solutions for x are x = -4/3 (approximately -1.33) and x = -32/3 (approximately -10.67).
Now, let's see which option matches these solutions:
A. {-10, 2}: Both values are present in the solutions we found.
B. {-2, 2}: None of these values are present in our solutions.
C. {-19, 11}: None of these values are present in our solutions.
D. {-22, -14}: None of these values are present in our solutions.
Therefore, the correct option is A. {-10, 2}.