Is there a value of x which satisfies the statement? How you can tell without finding, or attempting to find, the value.

Question

Is there a value of x which satisfies the statement? How you can tell without finding, or attempting to find, the value.

(x+10)= 6

1- Yes, because there are numbers whose distance from -10 on the number line is 6 .

2- No, because there is a number whose absolute value is 10

3- Yes, because there is a number whose absolute value is 10.

4- No, because there are numbers whose distance from -10 on the number line is 6.

5-No, because (x+10) cannot be negative.

Answer 1

You seem to be using parentheses to indicate absolute value. IF so, then

since 6 is positive, there is a number x+10 whose absolute value = 6

the answer is yes, so only 1 and 3 could be correct

1 is the best answer

x=-4 or -16, -16 is 6 from -10

also -4 is 6 from +10