Chapter 2

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I prefer interval notation over set-builder notation because it takes less space to write solution sets.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can check inequalities by substituting 0 for the variable: When 0 belongs to the solution set, I should obtain a true statement, and when 0 does not belong to the solution set,

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. In an inequality such as \(5 x+4<8 x-5,\) I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality \(-4 x<-20\) is equivalent to \(x>-5\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The statement "the sum of \(x\) and \(6 \%\) of \(x\) is at least 80 " is modeled by \(x+0.06 x \geq 80\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A car can be rented from Basic Rental for 260 dollars per week with no extra charge for mileage. Continental charges 80 dollars per week plus 25 cents for each mile driven to rent the same car. How many miles should be driven in a week to make the rental cost for Basic Rental a better deal than Continental's?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Membership in a fitness club costs 500 dollars yearly plus 1 dollars per hour spent working out. A competing club charges 440 dollars yearly plus 1.75 dollars per hour for use of their equipment. How many hours must a person work out yearly to make membership in the first club cheaper than membership in the second club?

Solve each inequality. Use a calculator to help with the arithmetic. \(1.45-7.23 x>-1.442\)

Solve each inequality. Use a calculator to help with the arithmetic. \(126.8-9.4 y \leq 4.8 y+34.5\)

8 is \(40 \%\) of what number?

The length of a rectangle exceeds the width by 5 inches. The perimeteris 34 inches. What are the rectangle's dimensions?

Solve and check: \(5 x+16=3(x+8)\).

Is \(x-4 y=14\) a true statement for \(x=2\) and \(y=-3 ?\)

Is \(x-4 y=14\) a true statement for \(x=12\) and \(y=1 ?\)

If \(y=\frac{2}{3} x+1,\) find the value of \(y\) for \(x=-6\)