1. 4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10
2. 11>-2 Add 5 to both sides, then add 3, then add (-4)
3. -4<-2 Subtract 6 from both sides, then 8, and then 2
4. -8<8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
Can I get some help please I dont understand
If you multiply or divide an inequality by a negative number,
you MUST flip the sign!
In this case:
1.
4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10
7 * 6 * 3 * 10 = 1260 is positive number
You do not have to change the sign of inequality.
2.
11>-2 Add 5 to both sides, then add 3, then add (-4)
When you add or subtract any number ( positive or negative ) you do not have to change the sign of inequality.
3.
Same as 2.
4.
-8<8 Divide both sides by - 4, then by - 2 mean:
-8<8 * [ 1 / - 4 * ( - 2 ) ]
-8<8 * 1 / 2
If you multiply or divide an inequality by a positive number,
you do not have to change the sign of inequality.
The point of the exercise is to show that operations with inequations are the same
as those with equations, EXCEPT when you multiply or divide both sides by a
negative, you must also reverse the inequality sign
I will do #4
-8<8 , which is true
it says to divide both sides by -4
-8/-4 < 8/-4
2 < -2 , which is now false. How do we make it true???
2 > -2 , I reversed the inequality sign
I don't know why in the exercise they did not include a multiplication by a negative
to show the property. They should have!
Indeed
4.
-8<8 Divide both sides by - 4, then by - 2 mean:
Divide both sides by - 4 / - 2
Divide both sides by 8
If you multiply or divide an inequality by a positive number,
you do not have to change the sign of inequality.
-8/8<8/8
-1<1
Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
Sure, I can help you understand the effects of the operations and how they affect the inequality sign.
1. 4 < 7: When you multiply both sides by the same positive number, it does not affect the inequality sign. In this case, you multiplied both sides by 7, then 6, then 3, and finally 10. The inequality remains true because all the multipliers are positive and the numbers remain in the same order.
2. 11 > -2: Similar to the first example, adding or subtracting the same value from both sides does not change the inequality sign. You added 5, then 3, and finally -4. Again, the inequality remains true because the additions do not change the order of the numbers.
3. -4 < -2: Subtracting or adding the same value from both sides also does not affect the inequality sign. You subtracted 6, then 8, and finally 2. However, the inequality becomes false after subtracting 6 because -4 - 6 = -10, which is not less than -2.
4. -8 < 8: Dividing both sides by the same positive number also preserves the inequality sign. In this case, you divided both sides by -4, then -2. However, when you divide by a negative number, the inequality sign flips. So the inequality becomes -8 / -4 > 8 / -4, which simplifies to 2 > -2, which is true.
In summary, when you perform the same operation on both sides of an inequality, the inequality sign remains the same. However, when you multiply or divide by a negative number, the inequality sign flips. It's important to be aware of this when solving inequalities.