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Can we multiply 2 inequalities?
Yes your proof is correct. Excellent work reducing the question about multiplying inequalities to a more familiar one of adding inequalities.
When can I multiply inequalities?
Well, one of those rules is called the multiplication property of inequality, and it basically says that if you multiply one side of an inequality by a number, you can multiply the other side of the inequality by the same number. However, you have to be very careful about the direction of the inequality!
What is multiplication property of inequality?
Well, one of those rules is called the multiplication property of inequality, and it basically says that if you multiply one side of an inequality by a number, you can multiply the other side of the inequality by the same number.
Can we add inequalities?
First of all, we can add inequalities with the same direction. In other words, with the inequalities pointing in the same direction. So if a is greater than b and c is greater than d, then we can just add them together. For example, 5 is greater than 2 and 11 is greater than 8, those are two true inequalities.
What is an inequality in math example?
An inequality is a mathematical relationship between two expressions and is represented using one of the following: ≤: “less than or equal to” <: “less than” ≠: “not equal to”
Can you multiply or divide an inequality by a negative number?
Answer)There is one very important exception to the rule that multiplying or dividing an inequality is the same as multiplying or dividing an equation. Whenever you multiply or divide any given inequality by any negative number, you must be able to flip the inequality sign.
How do you solve simple inequalities in math?
You can solve simple inequalities by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. When we multiply or divide both the sides by a negative number. When we swap the right hand sides and the left hand sides.
Is it possible to multiply inequalities with logarithms?
Yes your proof is correct. Excellent work reducing the question about multiplying inequalities to a more familiar one of adding inequalities. The only thing I would mention is that taking logarithms and exponentiating are monotone increasing operations. If they were monotone decreasing, the inequalities would flip.
What is the rebutal for the inequality sign change?
Rebuttal: If we square both sides of the inequality, we get a 2 b 2 > c 2 d 2 \\dfrac {a^2} {b^2} > \\dfrac {c^2} {d^2} b 2 a 2 > d 2 c 2 . Then we can cross multiply both sides by b 2 d 2 b^2 d^2 b 2 d 2, which is a positive number, so the inequality sign does not need to be changed.