Answer :
Sure, let's solve [tex]\( 4|x+5| = 16 \)[/tex] step-by-step.
1. Start by isolating the absolute value.
[tex]\[ 4|x+5| = 16 \][/tex]
2. Divide both sides by 4.
[tex]\[ |x+5| = 4 \][/tex]
3. Now, consider the definition of absolute value.
The equation [tex]\( |x+5| = 4 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 4 or -4.
4. Solve for the two cases:
- Case 1:
[tex]\[ x + 5 = 4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2:
[tex]\[ x + 5 = -4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
5. So, the solutions are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Therefore, the correct answer is:
B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]
1. Start by isolating the absolute value.
[tex]\[ 4|x+5| = 16 \][/tex]
2. Divide both sides by 4.
[tex]\[ |x+5| = 4 \][/tex]
3. Now, consider the definition of absolute value.
The equation [tex]\( |x+5| = 4 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 4 or -4.
4. Solve for the two cases:
- Case 1:
[tex]\[ x + 5 = 4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 4 - 5 \][/tex]
[tex]\[ x = -1 \][/tex]
- Case 2:
[tex]\[ x + 5 = -4 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = -4 - 5 \][/tex]
[tex]\[ x = -9 \][/tex]
5. So, the solutions are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Therefore, the correct answer is:
B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]