Answer:
D. x = -74 and x = 80
Step-by-step explanation:
Given equation:
[tex]\dfrac{1}{7}|x-3|-2=9[/tex]
The vertical lines mean absolute value.
The absolute value of a number is its positive numerical value.
To solve an equation containing an absolute value, isolate the absolute value on one side of the equation:
[tex]\implies \dfrac{1}{7}|x-3|-2=9[/tex]
Add 2 to both sides:
[tex]\implies \dfrac{1}{7}|x-3|-2+2=9+2[/tex]
[tex]\implies \dfrac{1}{7}|x-3|=11[/tex]
Multiply both sides by 7:
[tex]\implies 7 \cdot \dfrac{1}{7}|x-3|=7 \cdot 11[/tex]
[tex]\implies |x-3|=77[/tex]
Now set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation and solve the equations:
[tex]\begin{aligned}\textsf{\underline{Equation 1}} && \quad \quad\textsf{\underline{Equation 2}}\\x-3 & =77 & x-3& =-77\\x-3+3&=77+3 & x-3+3 & = -77+3\\x & = 80 & x & = -74\end{aligned}[/tex]
Therefore, the solutions to the given equation are:
x = -74 and x = 80.
