What is the abs value of X plus 2 less than 9?
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If you mean the difference in terms of numerical value, then it is the positive faction minus the negative faction, which is calculated as the positive fraction plus the absolute value* of the negative fraction - just like the difference between a positive and negative number. * The absolute value of a number is the value of the number ignoring any minus sign; eg abs(-4) = 4 = abs(4). If you mean the difference in terms of where they are on the number line, then the positive fraction is one side of zero (it is greater than zero) and the negative fraction is the other side of zero (it is less than zero).
-6 + abs(-11) = -6 + 11 = 5
abs(n - 6) < 9.
That is how the absolute value is defined. For x < 0 the value of x is negative (by definition). Therefore, the value of negative x is positive (negative of a negative). So abs(x) = -x when x < 0
ax + b = 15 or ax + b = -15