Answer :
Sure! Let's solve the equation step-by-step:
The given equation is:
[tex]\[ 4|x+5| = 28 \][/tex]
1. Isolate the absolute value term: Divide both sides of the equation by 4 to simplify it:
[tex]\[ |x + 5| = \frac{28}{4} \][/tex]
[tex]\[ |x + 5| = 7 \][/tex]
2. Set up two separate equations: The absolute value equation [tex]\( |x+5| = 7 \)[/tex] means that the expression inside the absolute value can be either 7 or -7. Therefore, we have two cases to consider:
- Case 1: [tex]\( x + 5 = 7 \)[/tex]
- Case 2: [tex]\( x + 5 = -7 \)[/tex]
3. Solve each case:
- For Case 1, solve:
[tex]\[ x + 5 = 7 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 7 - 5 \][/tex]
[tex]\[ x = 2 \][/tex]
- For Case 2, solve:
[tex]\[ x + 5 = -7 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -7 - 5 \][/tex]
[tex]\[ x = -12 \][/tex]
4. Write the solutions: The solutions to the equation are:
[tex]\[ x = 2 \][/tex]
and
[tex]\[ x = -12 \][/tex]
So, the correct answer is:
D. [tex]\( x = -12 \)[/tex] and [tex]\( x = 2 \)[/tex]
The given equation is:
[tex]\[ 4|x+5| = 28 \][/tex]
1. Isolate the absolute value term: Divide both sides of the equation by 4 to simplify it:
[tex]\[ |x + 5| = \frac{28}{4} \][/tex]
[tex]\[ |x + 5| = 7 \][/tex]
2. Set up two separate equations: The absolute value equation [tex]\( |x+5| = 7 \)[/tex] means that the expression inside the absolute value can be either 7 or -7. Therefore, we have two cases to consider:
- Case 1: [tex]\( x + 5 = 7 \)[/tex]
- Case 2: [tex]\( x + 5 = -7 \)[/tex]
3. Solve each case:
- For Case 1, solve:
[tex]\[ x + 5 = 7 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 7 - 5 \][/tex]
[tex]\[ x = 2 \][/tex]
- For Case 2, solve:
[tex]\[ x + 5 = -7 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -7 - 5 \][/tex]
[tex]\[ x = -12 \][/tex]
4. Write the solutions: The solutions to the equation are:
[tex]\[ x = 2 \][/tex]
and
[tex]\[ x = -12 \][/tex]
So, the correct answer is:
D. [tex]\( x = -12 \)[/tex] and [tex]\( x = 2 \)[/tex]