Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The first step in solving $\sqrt{x+6}=x+2$ is to square both sides, obtaining $x+6=x^2+4$.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 2800 pounds. If the elevator operator weighs 265 pounds and each cement bag weighs 65 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I solve an equation that is quadratic in form, it's important to write down the substitution that I am making.

If $x$ represents a number, note an English sentence about the number that results in an inconsistent equation.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The equation $5 x^{\frac{2}{3}}+11 x^{\frac{1}{3}}+2=0$ is quadratic in form, but when I reverse the variable terms and obtain $11 x^{\frac{1}{3}}+5 x^{\frac{2}{3}}+2=0$, the resulting equation is no longer quadratic in form.

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells personalized stationery. The weekly fixed cost is $\$ 3000$ and it costs $\$ 3.00$ to produce each package of stationery. The selling price is $\$ 5.50$ per package. How many packages of stationery must be produced and sold each week for the company to generate a profit?