I really don't understand please help with answers and explanations.
Follow the instructions for the following inequalities.
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?
4<7 Multiply both sides by 7
4 < 7
4*7 < 7*7 or, 28 < 49
-8<8 Divide both sides by -4
-8/-4 < 8/-4
2 < -2
Nope. 2 > -2
what happened? when you multiply/divide by a negative value, you switch the direction of the inequality. It's really just a shorthand way of moving something to the other side.
Other than that, as long as you do the same thing to both sides, the inequality remains true.
What about 2 and 3 how will I go about answering those?
Sure, I can help you understand the given instructions and the effects of the operations on the inequalities.
1. For the inequality 4 < 7, if you multiply both sides by 7, the inequality becomes 28 < 49. Then, if you multiply both sides by 6, the inequality becomes 168 < 294. By multiplying both sides by 3, the inequality becomes 504 < 882. Finally, if you multiply both sides by 10, the inequality becomes 5040 < 8820.
The effect of multiplying both sides by positive factors is that the inequality sign remains the same (in this case, "<") and the inequality still holds true since each operation maintains the relative value of the numbers.
2. For the inequality 11 > -2, if you add 5 to both sides, the inequality becomes 16 > 3. Then, adding 3 to both sides gives 19 > 6. Lastly, adding (-4) to both sides results in 15 > 2.
Similar to the multiplication example, adding positive numbers to both sides does not change the inequality sign (">") and the inequality remains true after each operation.
3. For the inequality -4 < -2, if you subtract 6 from both sides, the inequality becomes -10 < -8. Then, subtracting 8 from both sides gives -18 < -16. Finally, subtracting 2 from both sides results in -20 < -18.
Again, subtracting the same values from both sides keeps the inequality sign ("<") and the inequality still holds true.
4. For the inequality -8 < 8, if you divide both sides by -4, the inequality becomes 2 > -2. Then, dividing both sides by -2 gives -1 < 1.
Dividing both sides by negative factors inverses the inequality sign ("<" becomes ">"), and the inequality remains true.
Overall, the effects of the operations on the inequalities depend on the properties of the operations being applied. When dealing with inequalities, it's important to perform the same operation on both sides while considering the signs and properties involved to maintain the rules of inequalities and preserve the truth of the inequality statement.