Answer :
To solve the equation
[tex]$$
4|x-5| + 3 = 15,
$$[/tex]
follow these steps:
1. Subtract 3 from both sides:
This gives:
[tex]$$
4|x-5| = 15 - 3 = 12.
$$[/tex]
2. Divide both sides by 4:
Dividing by 4, we obtain:
[tex]$$
|x-5| = \frac{12}{4} = 3.
$$[/tex]
3. Solve the absolute value equation:
The equation
[tex]$$
|x-5| = 3
$$[/tex]
means that the expression inside the absolute value can be either [tex]$3$[/tex] or [tex]$-3$[/tex]. This leads to two cases:
- Case 1:
[tex]$$
x - 5 = 3 \quad \Longrightarrow \quad x = 5 + 3 = 8.
$$[/tex]
- Case 2:
[tex]$$
x - 5 = -3 \quad \Longrightarrow \quad x = 5 - 3 = 2.
$$[/tex]
4. Conclusion:
The solutions to the equation are:
[tex]$$
x = 2 \quad \text{and} \quad x = 8.
$$[/tex]
Thus, the values of [tex]$x$[/tex] for which [tex]$f(x)=15$[/tex] are [tex]$x=2$[/tex] and [tex]$x=8$[/tex].
[tex]$$
4|x-5| + 3 = 15,
$$[/tex]
follow these steps:
1. Subtract 3 from both sides:
This gives:
[tex]$$
4|x-5| = 15 - 3 = 12.
$$[/tex]
2. Divide both sides by 4:
Dividing by 4, we obtain:
[tex]$$
|x-5| = \frac{12}{4} = 3.
$$[/tex]
3. Solve the absolute value equation:
The equation
[tex]$$
|x-5| = 3
$$[/tex]
means that the expression inside the absolute value can be either [tex]$3$[/tex] or [tex]$-3$[/tex]. This leads to two cases:
- Case 1:
[tex]$$
x - 5 = 3 \quad \Longrightarrow \quad x = 5 + 3 = 8.
$$[/tex]
- Case 2:
[tex]$$
x - 5 = -3 \quad \Longrightarrow \quad x = 5 - 3 = 2.
$$[/tex]
4. Conclusion:
The solutions to the equation are:
[tex]$$
x = 2 \quad \text{and} \quad x = 8.
$$[/tex]
Thus, the values of [tex]$x$[/tex] for which [tex]$f(x)=15$[/tex] are [tex]$x=2$[/tex] and [tex]$x=8$[/tex].
