Select among the following the two operations that will not change the direction of an inequality.(1 point)
A negative number is added to both sides of an inequality.
A negative number is subtracted from both sides of an inequality.
A negative number is multiplied to both sides of an inequality.
A negative number is divided from both sides of an inequality.
The sign of every term on both sides of the inequality are changed to its opposite.
You ONLY change the arrow direction if you multiply (including divide which is just another way of saying multiply) both sides by a negative quantity ! The last choice is exactly the same as the two above it.
A negative number is added to both sides of an inequality and a negative number is subtracted from both sides of an inequality will not change the direction of an inequality.
The two operations that will not change the direction of an inequality are:
1. A negative number is added to both sides of an inequality.
2. A negative number is subtracted from both sides of an inequality.
To determine which operations will not change the direction of an inequality, we need to understand how inequalities behave under different operations.
1. Adding a negative number to both sides of an inequality:
When we add a negative number to both sides of an inequality, it does not change the direction of the inequality. For example, if we have the inequality x > 5, adding -3 to both sides gives x - 3 > 2. The direction of the inequality stays the same.
2. Subtracting a negative number from both sides of an inequality:
Subtracting a negative number is equivalent to adding a positive number. Therefore, like adding a negative number, subtracting a negative number also does not change the direction of the inequality. For example, if we have x < 7, subtracting -2 from both sides gives x + 2 < 9.
3. Multiplying both sides of an inequality by a negative number:
When we multiply both sides of an inequality by a negative number, the direction of the inequality is reversed. For example, if we have x > 3 and multiply both sides by -2, we get -2x < -6. The direction of the inequality changes from "greater than" to "less than."
4. Dividing both sides of an inequality by a negative number:
Similar to multiplication, dividing both sides of an inequality by a negative number also changes the direction of the inequality. For example, if we have x < 9 and divide both sides by -3, we get -3x > -27. The direction of the inequality changes from "less than" to "greater than."
5. Changing the sign of every term on both sides of the inequality to its opposite:
When we change the sign of every term on both sides of the inequality, it does not change the direction of the inequality. For example, if we have x > 4, changing the sign of every term gives -x < -4. The direction of the inequality remains the same.
From these explanations, we can conclude that the two operations that will not change the direction of an inequality are:
1. Adding a negative number to both sides of an inequality.
2. Changing the sign of every term on both sides of the inequality to its opposite.