91Ó°ÊÓ

In Exercises 71-76, use set-builder notation to describe all real numbers satisfying the given conditions. A number increased by 5 is at least two times the number.

Solve each proportion and check. \(\frac{2}{y-5}=\frac{3}{y+6}\)

It was wartime when the Ricardos found out Mrs. Ricardo was pregnant. Ricky Ricardo was drafted and made out a will, deciding that \(\$ 14,000\) in a savings account was to be divided between his wife and his child-to-be. Rather strangely, and certainly with gender bias, Ricky stipulated that if the child were a boy, he would get twice the amount of the mother's portion. If it were a girl, the mother would get twice the amount the girl was to receive. We'll never know what Ricky was thinking of, for (as fate would have it) he did not return from the war. Mrs. Ricardo gave birth to twins \(-\) a boy and a girl. How was the money divided?

A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after another. To each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more. Finally, the thief leaves the nursery with 1 lone palm. How many plants were originally stolen?

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(2(x-5)=2 x+10\)

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(2(x+4)=4 x+5-2 x+3\)

Use set-builder notation to describe all real numbers satisfying the given conditions. If the quotient of three times a number and five is increased by four, the result is no more than 34 .

What is a term? Provide an example with your description.

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(7+2(3 x-5)=8-3(2 x+1)\)

Make Sense? Determine whether each statement makes sense or does not make sense, and explain your reasoning. Regardless of what real numbers I substitute for \(x\) and \(y\), I will always obtain zero when evaluating \(2 x^{2} y-2 y x^{2}\).