# Explain how solving -7y > 161 is different from solving 7y > -161.

Hi!  Feel free to use either answer.   My It is different because you get a different answer when you multiply or divide when the negative sign is in a different position. If y equals 2, the first inequality is incorrect because -14 is less than 161, not greater. But in the second equation, 14 is greater than -161, so the other inequality is correct. So when the negative sign gets switched/moved around to each number, the positive and negative values of each number swap. Sample response: Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>
Hope this helps!

Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>

Explanation: The method of solution is substantially the same, but there is a detail that needs to be attended to. If the solution method in the first case is to divide by the coefficient of y, then that division (or multiplication) by a negative number changes the ordering. The “>” symbol needs to be reversed to a “<" symbol.   -7y > 161   y < -23 . . . . . . after division by -7 __ In the second case, dividing by the coefficient of y gives ...   7y > -161   y > 23 . . . . . . . no reordering necessary for division by a positive number Alternate method for dealing with negative coefficients The equation in the first case can also be solved by adding 7y-161 to get …   -161 > 7y Now, division by 7 proceeds the same as in the second case, with no reordering required:   -23 > y ___ ___ ___ Personal note I was completely mystified by the solution of inequalities until I realized this rule. Multiplication or division by a negative number reverses the ordering. There are also some other operations that can be performed on inequalities that reverse the ordering. A simple example is taking the reciprocal. For an equation in which a=b, it is also true that 1/a = 1/b. For an inequality, …   a > b   1/a < 1/b . . . . . when a and b have the same sign, the ordering symbol is reversed Actually, any function in which the slope is negative in the relevant domain can require the ordering to be reversed. Trig functions can do that: for first and second quadrant angles, a > b means cos(a) < cos(b). What it amounts to is that you need to pay attention to ordering if you're doing anything other than addition and subtraction and multiplication by a positive number.

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magic Step-by-step explanation:

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idk Step-by-step explanation:

Sample response: Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>

EDGE 2020 Step-by-step explanation: Sample response: Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>

7y > -161…here u divide by 7y > -161/7y > -23

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