Let x represent the number.
2(x+7) = 3|x-2|
If x > 2,
2x + 14 = 3x - 6 (the absolute value bars do not change the sign)
20 = x (add 6-2x to both sides)
If x < 2,
2(x+7) = 3(-x+2) (the absolute value bars change the sign of their contents when contents are negative)
2x + 14 = -3x + 6 (use the distributive property to eliminate parentheses)
5x = -8 (add 3x-14 to both sides)
x = -1 3/5 (divide both sides by 5)
Possible values for the number are 20 and -1 3/5.
Check
2(20+7) = 3(20-2)
2*27 = 3*18
54 = 54 (yes, the first possibility checks)
2(-1 3/5 + 7) = 3(2 - (-1 3/5))
2(5 2/5) = 3(3 3/5)
10 4/5 = 9 9/5 (yes, the second possibility checks)
Note that when we say "the difference between 1 and 2", we usually mean +1, not -1. That is to say, we usually mean "the magnitude of the difference between 1 and 2." The above working of the problem reflects this ambiguity of language.
2(x+7) = 3|x-2|
If x > 2,
2x + 14 = 3x - 6 (the absolute value bars do not change the sign)
20 = x (add 6-2x to both sides)
If x < 2,
2(x+7) = 3(-x+2) (the absolute value bars change the sign of their contents when contents are negative)
2x + 14 = -3x + 6 (use the distributive property to eliminate parentheses)
5x = -8 (add 3x-14 to both sides)
x = -1 3/5 (divide both sides by 5)
Possible values for the number are 20 and -1 3/5.
Check
2(20+7) = 3(20-2)
2*27 = 3*18
54 = 54 (yes, the first possibility checks)
2(-1 3/5 + 7) = 3(2 - (-1 3/5))
2(5 2/5) = 3(3 3/5)
10 4/5 = 9 9/5 (yes, the second possibility checks)
Note that when we say "the difference between 1 and 2", we usually mean +1, not -1. That is to say, we usually mean "the magnitude of the difference between 1 and 2." The above working of the problem reflects this ambiguity of language.
