Chapter 2

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{x-2}{3 x+5} \leq 4 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ -2<\frac{4 x+1}{3} \leq 0 $$

Exer. 1-50: Solve the equation. $$ \sqrt{5 \sqrt{x}}=\sqrt{2 x-3} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{5-\sqrt{-121}}{1+\sqrt{-25}} $$

Exer. \(31-44\) : Solve by using the quadratic formula. $$ 5 x^{2}+13 x=6 $$

It takes a girl 45 minutes to deliver the newspapers on her route; however, if her brother helps, it takes them only 20 minutes. How long would it take her brother to deliver the newspapers by himself?

Solve the equation. $$(x+3)^{3}-(3 x-1)^{2}=x^{3}+4$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{x+1}{2 x-3}>2 $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 4>\frac{2-3 x}{7} \geq-2 $$

Exer. 1-50: Solve the equation. $$ \sqrt{1+4 \sqrt{x}}=\sqrt{x}+1 $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{\sqrt{-36} \sqrt{-49}}{\sqrt{-16}} $$

Exer. \(31-44\) : Solve by using the quadratic formula. $$ x^{2}+4 x+2=0 $$

A water tank can be emptied by using one pump for 5 hours. A second, smaller pump can empty the tank in 8 hours. If the larger pump is started at 1:00 P.M., at what time should the smaller pump be started so that the tank will be emptied at 5:00 P.M.?

Solve the equation. $$(x-1)^{3}=(x+1)^{3}-6 x^{2}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{2}{2 x+3} \leq \frac{2}{x-5} $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 5 \geq \frac{6-5 x}{3}>2 $$

Exer. 1-50: Solve the equation. $$ \sqrt{x+1}=\sqrt{x-1} $$

Exer. 1-34: Write the expression in the form \(a+b i\), where \(a\) and \(b\) are real numbers. $$ \frac{\sqrt{-25}}{\sqrt{-16} \sqrt{-81}} $$

Exer. \(31-44\) : Solve by using the quadratic formula. $$ x^{2}-6 x-3=0 $$

A college student has finished 48 credit hours with a GPA of \(2.75\). To get into the program she wishes to enter, she must have a GPA of 3.2. How many additional credit hours of \(4.0\) work will raise her GPA to \(3.2\) ?

Solve the equation. $$\frac{9 x}{3 x-1}=2+\frac{3}{3 x-1}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{4}{3 x-2} \leq \frac{2}{x+1} $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ 0 \leq 4-\frac{1}{3} x<2 $$

Exer. 1-50: Solve the equation. $$ x^{4}-25 x^{2}+144=0 $$

Exer. 35-38: Find the values of \(x\) and \(y\), where \(x\) and \(y\) are real numbers. $$ 4+(x+2 y) i=x+2 i $$

Exer. \(31-44\) : Solve by using the quadratic formula. $$ 2 x^{2}-3 x-4=0 $$

In electrical theory, Ohm's law states that \(I=V / R\), where \(I\) is the current in amperes, \(V\) is the electromotive force in volts, and \(R\) is the resistance in ohms. In a certain circuit \(V=110\) and \(R=50\). If \(V\) and \(R\) are to be changed by the same numerical amount, what change in them will cause \(I\) to double?

Solve the equation. $$\frac{2 x}{2 x+3}+\frac{6}{4 x+6}=5$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{3}{5 x+1} \geq \frac{1}{x-3} $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ -2<3+\frac{1}{4} x \leq 5 $$

Exer. 1-50: Solve the equation. $$ 2 x^{4}-10 x^{2}+8=0 $$

Exer. 35-38: Find the values of \(x\) and \(y\), where \(x\) and \(y\) are real numbers. $$ (x-y)+3 i=7+y i $$

Exer. \(31-44\) : Solve by using the quadratic formula. $$ 3 x^{2}+5 x+1=0 $$

Below the cloud base, the air temperature \(T\) (in \({ }^{\circ} \mathrm{F}\) ) at height \(h\) (in feet) can be approximated by the equation \(T=T_{0}-\left(\frac{55}{1000}\right) h\), where \(T_{0}\) is the temperature at ground level. (a) Determine the air temperature at a height of 1 mile if the ground temperature is \(70^{\circ} \mathrm{F}\). (b) At what altitude is the temperature freezing?

Solve the equation. $$\frac{1}{x+4}+\frac{3}{x-4}=\frac{3 x+8}{x^{2}-16}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ \frac{x}{3 x-5} \leq \frac{2}{x-1} $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ (2 x-3)(4 x+5) \leq(8 x+1)(x-7) $$

Exer. 1-50: Solve the equation. $$ 5 y^{4}-7 y^{2}+1=0 $$

Exer. 35-38: Find the values of \(x\) and \(y\), where \(x\) and \(y\) are real numbers. $$ (2 x-y)-16 i=10+4 y i $$

Exer. \(31-44\) : Solve by using the quadratic formula. $$ \frac{3}{2} z^{2}-4 z-1=0 $$

The height \(h\) (in feet) of the cloud base can be estimated using \(h=227(T-D)\), where \(T\) is the ground temperature and \(D\) is the dew point. (a) If the temperature is \(70^{\circ} \mathrm{F}\) and the dew point is \(55^{\circ} \mathrm{F}\), find the height of the cloud base. (b) If the dew point is \(65^{\circ} \mathrm{F}\) and the cloud base is 3500 feet, estimate the ground temperature.

Solve the equation. $$\frac{2}{2 x+3}+\frac{4}{2 x-3}=\frac{5 x+6}{4 x^{2}-9}$$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ (x-3)(x+3) \geq(x+5)^{2} $$

Exer. 1-50: Solve the equation. $$ 3 y^{4}-5 y^{2}+1=0 $$

Exer. 35-38: Find the values of \(x\) and \(y\), where \(x\) and \(y\) are real numbers. $$ 8+(3 x+y) i=2 x-4 i $$

Exer. \(31-44\) : Solve by using the quadratic formula. $$ \frac{5}{3} s^{2}+3 s+1=0 $$

The temperature \(T\) within a cloud at height \(h\) (in feet) above the cloud base can be approximated using the equation \(T=B-\left(\frac{3}{1000}\right) h\), where \(B\) is the temperature of the cloud at its base. Determine the temperature at 10,000 feet in a cloud with a base temperature of \(55^{\circ} \mathrm{F}\) and a base height of 4000 feet. Note: For an interesting application involving the three preceding exercises, see Exercise 6 in the Discussion Exercises at the end of the chapter.

Solve the equation. $$\frac{4}{x+2}+\frac{1}{x-2}=\frac{5 x-6}{x^{2}-4}$$

Exer. 1-40: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ x^{3}>x $$

Exer. 21-70: Solve the inequality, and express the solutions in terms of intervals whenever possible. $$ (x-4)^{2}>x(x+12) $$