Respuesta :

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Solve for x over the integers:
abs(16 - x) = 18
Split the equation into two possible cases:
16 - x = 18 or 16 - x = -18
Subtract 16 from both sides:
-x = 2 or 16 - x = -18
Multiply both sides by -1:
x = -2 or 16 - x = -18
Subtract 16 from both sides:
x = -2 or -x = -34
Multiply both sides by -1:
Answer:  x = -2 or x = 34

Answer:

Option 2 - The required solution is -2 and 34.

Step-by-step explanation:

Given : Equation, [tex]|16-x|=18[/tex]

To find : Solve the equation with the replacement set {–34, –2, 2, 34}  ?

Solution :

The equation [tex]|16-x|=18[/tex] is written as,

[tex]16-x=18[/tex] and [tex]16-x=-18[/tex]

Substitute the values from set if it satisfy the equation that is the solution,

1) Put x=-34,

[tex]16-(-34)=16+34=50\neq 18[/tex]

Not true.

2) Put x=-2,

[tex]16-x=16-(-2)=16+2=18[/tex]

True.

3) Put x=2,

[tex]16-x=16-(2)=14\neq 18[/tex]

Not true.

4) Put x=34

[tex]16-x=16-(34)=-18[/tex]

True.

Therefore, The required solution is -2 and 34.

So, Option 2 is correct.

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