Section 1
Equations and Inequalities
Solve and check each equation.$$1.2 x+10=40$$
Solve and check each equation.$$-3 y+20=2$$
Solve and check each equation.$$5 x+2=2 x-10$$
Solve and check each equation.$$4 x-11=7 x+20$$
Solve and check each equation.$$2(x-3)-5=4(x-5)$$
Solve and check each equation.$$6(5 s-11)-12(2 s+5)-0$$
Solve and check each equation.$$\frac{3}{4} x+\frac{1}{2}=\frac{2}{3}$$
Solve and check each equation.$$\text { 8. } \frac{x}{4}-5=\frac{1}{2}$$
Solve and check each equation.$$\frac{2}{3} x-5=\frac{1}{2} x-3$$
Solve and check each equation.$$\frac{1}{2} x+7-\frac{1}{4} x=\frac{19}{2}$$
Solve and check each equation.$$0.2 x+0.4=3.6$$
Solve and check each equation.$$0.04 x-0.2=0.07$$
Solve and check each equation.$$\frac{3}{5}(n+5)-\frac{3}{4}(n-11)=0$$
Solve and check each equation.$$-\frac{5}{7}(p+11)+\frac{2}{5}(2 p-5)=0$$
Solve and check each equation.$$3(x+5)(x-1)-(3 x+4)(x-2)$$
Solve and check each equation.$$5(x+4)(x-4)=(x-3)(5 x+4)$$
Solve and check each equation.$$0.08 x+0.12(4000-x)=432$$
Solve and check each equation.$$0.075 y+0.06(10,000-y)-727.50$$
solve each quadratic equation by factoring and applying the zero product property.$$x^{2}-2 x-15=0$$
solve each quadratic equation by factoring and applying the zero product property.$$y^{2}+3 y-10=0$$
solve each quadratic equation by factoring and applying the zero product property.$$8 y^{2}+189 y-72=0$$
solve each quadratic equation by factoring and applying the zero product property.$$12 w^{2}-41 w+24=0$$
solve each quadratic equation by factoring and applying the zero product property.$$3 x^{2}-7 x-0$$
solve each quadratic equation by factoring and applying the zero product property.$$5 x^{2}=-8 x$$
solve each quadratic equation by factoring and applying the zero product property.$$(x-5)^{2}-9=0$$
solve each quadratic equation by factoring and applying the zero product property.$$(3 x+4)^{2}-16=0$$
Solve by completing the square or by using the quadratic formula.$$x^{2}-2 x-15=0$$
Solve by completing the square or by using the quadratic formula.$$x^{2}-5 x-24=0$$
Solve by completing the square or by using the quadratic formula.$$x^{2}+x-1=0$$
Solve by completing the square or by using the quadratic formula.$$x^{2}+x-2=0$$
Solve by completing the square or by using the quadratic formula.$$2 x^{2}+4 x+1=0$$
Solve by completing the square or by using the quadratic formula.$$2 x^{2}+4 x-1=0$$
Solve by completing the square or by using the quadratic formula.$$3 x^{2}-5 x-3=0$$
solve by completing the square or by using the quadratic formula.$$3 x^{2}-5 x-4=0$$
solve by completing the square or by using the quadratic formula.$$\frac{1}{2} x^{2}+\frac{3}{4} x-1=0$$
Solve by completing the square or by using the quadratic formula.$$\frac{2}{3} x^{2}-5 x+\frac{1}{2}=0$$
Solve by completing the square or by using the quadratic formula.$$\sqrt{2} x^{2}+3 x+\sqrt{2}-0$$
Solve by completing the square or by using the quadratic formula.$$2 x^{2}+\sqrt{5} x-3=0$$
Solve by completing the square or by using the quadratic formula.$$x^{2}-3 x+5$$
Solve by completing the square or by using the quadratic formula.$$-x^{2}-7 x-1$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$2 x+3<11$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$3 x-5>16$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$x+4>3 x+16$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$5 x+6<2 x+1$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$-6 x+1 \geq 19$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$-5 x+2 \leq 37$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$-3(x+2) \leq 5 x+7$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$-4(x-5)=2 x+15$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$-4(3 x-5)>2(x-4)$$
Use the properties of inequalities to solve each inequality. Write answers using interval notation.$$3(x+7) \leq 5(2 x-8)$$
Solve each quadratic inequality. Use interval notation to write each solution set.$$x^{2}+7 x>0$$
Solve each quadratic inequality. Use interval notation to write each solution set.$$x^{2}-5 x \leq 0$$
Solve each quadratic inequality. Use interval notation to write each solution set.$$x^{2}+7 x+10<0$$
Solve each quadratic inequality. Use interval notation to write each solution set.$$x^{2}+5 x+6<0$$
Solve each quadratic inequality. Use interval notation to write each solution set.$$x^{2}-3 x \geq 28$$
Solve each quadratic inequality. Use interval notation to write each solution set.$$x^{2}<-x+30$$
Solve each quadratic inequality. Use interval notation to write each solution set.$$6 x^{2}-4 \leq 5 x$$
Solve each quadratic inequality. Use interval notation to write each solution set.$$12 x^{2}+8 x=15$$
Use interval notation to express the solution set of each inequality.$$|x|<4$$
Use interval notation to express the solution set of each inequality.$$|x|>2$$
Use interval notation to express the solution set of each inequality.$$|x-1|<9$$
Use interval notation to express the solution set of each inequality.$$|x-3|<10$$
Use interval notation to express the solution set of each inequality.$$|x+3|>30$$
Use interval notation to express the solution set of each inequality.$$|x+4|<2$$
Use interval notation to express the solution set of each inequality.$$|2 x-1|>4$$
Use interval notation to express the solution set of each inequality.$$|2 x-9|<7$$
Use interval notation to express the solution set of each inequality.$$|x+3| \geq 5$$
Use interval notation to express the solution set of each inequality.$$|x-10| \geq 2$$
Use interval notation to express the solution set of each inequality.$$|3 x-10| \leq 14$$
Use interval notation to express the solution set of each inequality.$$|2 x-5| \geq 1$$
Use interval notation to express the solution set of each inequality.$$|4-5 x| \geq 24$$
Use interval notation to express the solution set of each inequality.$$|3-2 x| \leq 5$$
Use interval notation to express the solution set of each inequality.$$|x-5| \geq 0$$
Use interval notation to express the solution set of each inequality.$$|x-7| \geq 0$$
Use interval notation to express the solution set of each inequality.$$|x-4| \leq 0$$
Use interval notation to express the solution set of each inequality.$$|2 x+7| \leq 0$$
The perimeter of a rectangle is 27 centimeters, and its area is 35 square centimeters. Find the length and the width of the rectangle.
The perimeter of a rectangle is 34 feet and its area is 60 square feet. Find the length and the width of the rectangle.
A gardener wishes to use 600 feet of fencing to enclose a rectangular region and subdivide the region into two smaller rectangles. The total enclosed area is 15,000 square feet. Find the dimensions of the enclosed region.
A farmer wishes to use 400 yards of fencing to enclose a rectangular region and subdivide the region into three smaller rectangles. If the total enclosed area is 4800 square yards, find the dimensions of the enclosed region.(Figure cant copy)
A bank offers two checking account plans. The monthly fee and charge per check for each plan are shown below. Under what conditions is it less expensive to use the Low Charge plan?(Table cant copy)
You can rent a car for the day from company A for $\$ 29.00$ plus $\$ 0.12$ a mile. Company B charges $\$ 22.00$ plus $\$ 0.21$ a mile. Find the number of miles $m$ (to the nearest mile) per day for which it is cheaper to rent from company A.
A sales clerk has a choice between two payment plans. Plan A pays $\$ 100.00$ a week plus $\$ 8.00$ a sale. Plan B pays $\$ 250.00$ a week plus $\$ 3.50$ a sale. How many sales per week must be made for plan A to yield the greater paycheck?
A video store offers two rental plans. The yearly membership fee and the daily charge per video are shown below. How many videos can be rented per year if the No-fee plan is to be the less expensive of the plans?(Table cant copy)
The average daily minimum-tomaximum temperatures for the city of Palm Springs during the month of September are $68^{\circ} \mathrm{F}$ to $104^{\circ} \mathrm{F}$. What is the corresponding temperature range measured on the Celsius temperature scale?
The ancient Greeks defined a rectangle as a “golden rectangle” if its length l and its width w satisfied the equation$$\frac{1}{u v}=\frac{u}{l-u v}$$a. Solve this formula for w.b. If the length of a golden rectangle is 101 feet, determine its width. Round to the nearest hundredth.
The sum $S$ of the first $n$ natural numbers $1,2,3, \ldots, n$ is given by the formula$$S=\frac{n}{2}(n+1)$$How many consecutive natural numbers starting with 1 produce a sum of 253?
The number of diagonals $D$ of a polygon with $n$ sides is given by the formula$$D=\frac{n}{2}(n-3)$$a. Determine the number of sides of a polygon with 464 diagonals.b. Can a polygon have 12 diagonals? Explain.
The monthly revenue $R$ for a product is given by $R-420 x-2 x^{2},$ where $x$ is the price in dollars of each unit produced. Find the interval in terms of $x$ for which the monthly revenue is greater than zero.
Write an absolute value inequality to represent all real numbers withina. 8 units of 3b. $k$ units of $j$ (assume $k>0$ )
The equation$$s=-16 t^{2}+v_{0} t+s_{0}$$gives the height $s$, in feet above ground level, of an object t seconds after the object is thrown directly upward from a height $s_{0}$ feet above the ground with an initial velocity of $v_{0}$ feet per second. A ball is thrown directly upward from ground level with an initial velocity of 64 feet per second. Find the time interval during which the ball has a height of more than 48 feet.
A ball is thrown directly upward from a height of 32 feet above the ground with an initial velocity of 80 feet per second. Find the time interval during which the ball will be more than 96 feet above the ground. (Hint: See Exercise 91.)(Figure cant copy)
The length of the side of a square has been measured accurately to within 0.01 foot. This measured length is 4.25 feet.a. Write an absolute value inequality that describes the relationship between the actual length of each side of the square s and its measured length.b. Solve the absolute value inequality you found in part a. for s.
Evaluate $\frac{x_{1}+x_{2}}{2}$ when $x_{1}=4$ and $x_{2}=-7.$
Simplify $\sqrt{50} .[\mathrm{A} .1]$
Is $y=3 x-2$ a true equation when $y-5$ and $x=-1 ?$ [1.1]
If $y=x^{2}-3 x+2,$ find $x$ when $y=0 .[1.1]$
Evaluate $|-x-y|$ when $x-3$ and $y=-1 .[1.1]$
Evaluate $\sqrt{a^{2}+b^{2}}$ when $a=-3$ and $b=4 .[\text { A. } 1]$