Question

Solve for x: 1/7 (x - 3) - 2 = 9

A. x = 74 and x = 80
B. x = -46 and x =52
C. x = -52 and x = 46
D. x= -74 and x = 80

Answer 1

D. x = -74 and x = 80

Explanation:

Given equation:

`(1)/(7)|x-3|-2=9`

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:

`\implies (1)/(7)|x-3|-2=9`

Add 2 to both sides:

`\implies (1)/(7)|x-3|-2+2=9+2`

`\implies (1)/(7)|x-3|=11`

Multiply both sides by 7:

`\implies 7 \cdot (1)/(7)|x-3|=7 \cdot 11`

`\implies |x-3|=77`

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:

`\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}`

Therefore, the solutions to the given equation are:

x = -74 and x = 80.

Answer 2

∑ Hey, zayzaygaming2009 ⊃

Answer:

D. x= -74 and x = 80

Explanation:

Given:

Solve for x: 1/7 (x - 3) - 2 = 9

A. x = 74 and x = 80

B. x = -46 and x =52

C. x = -52 and x = 46

D. x= -74 and x = 80

Solve:

I think you meant:
`(1)/(7)*|x - 3| - 2 = 9` because if you solve
`(1)/(7) (x - 3) - 2 = 9`the answer will be x= 80 but as I look at the answer choices it doesn't match.

This is a absolute value equation.

To solve this absolute value equation we have to isolate the absolute value part first. Which is;

⇒
`(1)/(7)*|x - 3| - 2 = 9`

⇒
`(1)/(7)*|x - 3| = 9 + 2`

⇒
`(1)/(7)*|x - 3| = 11`

⇒
`|x - 3| = 11*7`

⇒
`|x - 3| = 77`

Instantly, we can decompose the absolute value equation into two simpler ones below:

`x - 3 = 77x - 3 = -77`

Now we solve for x;

`x-3 =77`

`x-3+3=77+3`

`x=80`

and;

`x-3=-77`

`x-3+3=-77+3`

`x=-74`

Hence the solutions are;

x = -74 and x = 80

Which also means:

D. x = -74 and x = 80 is the correct answer.

xcookiex12

8/18/2022