Answer :
Sure! Let's solve the equation step-by-step:
The given equation to solve is:
[tex]\[ 4|x + 6| + 8 = 28 \][/tex]
1. Isolate the absolute value term:
Subtract 8 from both sides to isolate the term containing the absolute value:
[tex]\[ 4|x + 6| + 8 - 8 = 28 - 8 \][/tex]
[tex]\[ 4|x + 6| = 20 \][/tex]
2. Solve for the absolute value expression:
Divide both sides by 4 to further isolate the absolute value:
[tex]\[ \frac{4|x + 6|}{4} = \frac{20}{4} \][/tex]
[tex]\[ |x + 6| = 5 \][/tex]
3. Solve the absolute value equation:
An absolute value equation |A| = B means that A can be either B or -B. So, we have two cases to consider:
- Case 1:
[tex]\[ x + 6 = 5 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = 5 - 6 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2:
[tex]\[ x + 6 = -5 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = -5 - 6 \][/tex]
[tex]\[ x = -11 \][/tex]
4. Conclusion:
From the above steps, we have determined that the solutions to the equation [tex]\( 4|x + 6| + 8 = 28 \)[/tex] are:
[tex]\[ x = -1 \][/tex]
[tex]\[ x = -11 \][/tex]
So the correct answer is:
[tex]\[ \boxed{x = -1 \text{ and } x = -11} \][/tex]
Thus, the correct choice from the given options is:
[tex]\[ \text{A. } x = -1 \text{ and } x = -11 \][/tex]
The given equation to solve is:
[tex]\[ 4|x + 6| + 8 = 28 \][/tex]
1. Isolate the absolute value term:
Subtract 8 from both sides to isolate the term containing the absolute value:
[tex]\[ 4|x + 6| + 8 - 8 = 28 - 8 \][/tex]
[tex]\[ 4|x + 6| = 20 \][/tex]
2. Solve for the absolute value expression:
Divide both sides by 4 to further isolate the absolute value:
[tex]\[ \frac{4|x + 6|}{4} = \frac{20}{4} \][/tex]
[tex]\[ |x + 6| = 5 \][/tex]
3. Solve the absolute value equation:
An absolute value equation |A| = B means that A can be either B or -B. So, we have two cases to consider:
- Case 1:
[tex]\[ x + 6 = 5 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = 5 - 6 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2:
[tex]\[ x + 6 = -5 \][/tex]
Subtract 6 from both sides:
[tex]\[ x = -5 - 6 \][/tex]
[tex]\[ x = -11 \][/tex]
4. Conclusion:
From the above steps, we have determined that the solutions to the equation [tex]\( 4|x + 6| + 8 = 28 \)[/tex] are:
[tex]\[ x = -1 \][/tex]
[tex]\[ x = -11 \][/tex]
So the correct answer is:
[tex]\[ \boxed{x = -1 \text{ and } x = -11} \][/tex]
Thus, the correct choice from the given options is:
[tex]\[ \text{A. } x = -1 \text{ and } x = -11 \][/tex]