Question 1090670
<br>If you want to just blindly perform mathematical operations to answer this question, you can simply plug the x and y values of the given point into the two inequalities and see if both inequalities are satisfied.  The work might look something like this....<br>
{{{x-2y = (-3/2) - 2(1/3) = (-3/2) - (2/3) = (-9/6) - (4/6) = -13/6}}}
Yes, -13/6 is less than 4; the first inequality is satisfied.<br>
{{{abs(3x-1)+2 = abs(3(-3/2)-1)+2 = abs(-9/2-1)+2 = abs(-11/2)+2 = 11/2+2 = 11/2+4/2 = 15/2}}}
y = 1/3 is less than 15/2, so the second inequality is also satisfied.<br><br>
But you don't need to go to all that work.  You can use logical reasoning without any need to do any detailed calculations to see that both inequalities are satisfied.<br>
In the first inequality, you are starting with a negative value (x is negative), and you are subtracting a positive value (y is positive), so the result is clearly a negative number.  But you don't care what negative number it is, because ANY negative number is less than 4.<br>
For the second inequality, the value of the absolute value part of the expression on the right is 0 or positive; so when you add 2, the value of the entire expression on the right is 2 or greater.  And again you don't care what the exact value of the expression is for the given x value, because ANY number that is greater than or equal to 2 is greater than the given y value 1/3.