Chapter 1

Evaluate \(x^{2}-(x y-y)\) for \(x\) satisfying \(\frac{13 x-6}{4}=5 x+2\) and \(y\) satisfying \(5-y=7(y+4)+1\)

Suppose that we agree to pay you 8ç for every problem in this chapter that you solve correctly and fine you 5 ç for every problem done incorrectly. If at the end of 26 problems we do not owe each other any money, how many problems did you solve correctly?

Solve each equation in Exercises \(83-108\) by the method of your choice. $$2 x^{2}=250$$

This will help you prepare for the material covered in the next section. Multiply and simplify: \(12\left(\frac{x+2}{4}-\frac{x-1}{3}\right)\)

Solve absolute value inequality. \(1<|2-3 x|\)

solve each equation. $$ \left[(3+6)^{2}+3\right] \cdot 4=-54 x $$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$x^{2}-2 x=1$$

This will help you prepare for the material covered in the next section. Multiply and simplify: \((x-3)\left(\frac{3}{x-3}+9\right)\)

Solve absolute value inequality. \(4<|2-x|\)

solve each equation. $$ 2^{3}-\left[4(5-3)^{3}\right]=-8 x $$

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 in Exercises \(83-108\) by the method of your choice. $$2 x^{2}+3 x=1$$

Solve absolute value inequality. \(12<\left|-2 x+\frac{6}{7}\right|+\frac{3}{7}\)

solve each equation. $$ 5-12 x=8-7 x-\left[6 \div 3\left(2+5^{3}\right)+5 x\right] $$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$(2 x+3)(x+4)=1$$

Solve absolute value inequality. \(1<\left|x-\frac{11}{3}\right|+\frac{7}{3}\)

solve each equation. $$ 2(5 x+58)=10 x+4(21 \div 3.5-11) $$

One of the best ways to learn how to solve a word problem in algebra is to design word problems of your own. Creating a word problem makes you very aware of precisely how much information is needed to solve the problem. You must also focus on the best way to present information to a reader and on how much information to give. As you write your problem, you gain skills that will help you solve problems created by others The group should design five different word problems that can be solved using linear equations. All of the problems should be on different topics. For example, the group should not have more than one problem on simple interest. The group should turn in both the problems and their algebraic solutions.

Solve each equation in Exercises \(83-108\) by the method of your choice. $$(2 x-5)(x+1)=2$$

Solve absolute value inequality. \(4+\left|3-\frac{x}{3}\right| \geq 9\)

solve each equation. $$ 0.7 x+0.4(20)=0.5(x+20) $$

Exercises \(93-95\) will help you prepare for the material covered in the next section. $$ \text { Multiply: }(7-3 x)(-2-5 x) $$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$(3 x-4)^{2}=16$$

Solve absolute value inequality. \(\left|2-\frac{x}{2}\right|-1 \leq 1\)

solve each equation. $$ 0.5(x+2)=0.1+3(0.1 x+0.3) $$

Exercises \(93-95\) will help you prepare for the material covered in the next section. $$ \text { Simplify: } \sqrt{18}-\sqrt{8} $$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$(2 x+7)^{2}=25$$

solve each equation. $$ 4 x+13-|2 x-[4(x-3)-5]|=2(x-6) $$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$3 x^{2}-12 x+12=0$$

solve each equation. $$ -2[7-[4-2(1-x)+3] |=10-[4 x-2(x-3)] $$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$9-6 x+x^{2}=0$$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$4 x^{2}-16=0$$

Solve each equation. $$x(x+1)^{3}-42(x+1)^{2}-0$$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$3 x^{2}-27=0$$

Solve each equation. $$x(x-2)^{3}-35(x-2)^{2}-0$$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$x^{2}-6 x+13=0$$

Solve each equation. If 5 times a number is decreased by \(4,\) the principal square root of this difference is 2 less than the number. Find the number(s).

Solve each equation in Exercises \(83-108\) by the method of your choice. $$x^{2}-4 x+29=0$$

If a number is decreased by \(3,\) the principal square root of this difference is 5 less than the number. Find the number(s).

Solve each equation in Exercises \(83-108\) by the method of your choice. $$x^{2}-4 x=7$$

Solve for \(V: r-\sqrt{\frac{3 V}{\pi h}}\)

Solve for \(A: r-\sqrt{\frac{A}{4 \pi}}\)

Use the graph of \(y-|4-x|\) to solve each inequality. \(|4-x|<5\)

Solve each equation in Exercises \(83-108\) by the method of your choice. $$2 x^{2}-7 x=0$$

List all numbers that must be excluded from the domain of each expression. $$\frac{|x-1|-3}{|x+2|-14}$$

Use the graph of \(y-|4-x|\) to solve each inequality. \(|4-x| \geq 5\)

Solve each equation in Exercises \(83-108\) by the method of your choice. $$2 x^{2}+5 x=3$$

List all numbers that must be excluded from the domain of each expression. $$\frac{x^{3}-2 x^{2}-9 x+18}{x^{3}+3 x^{2}-x-3}$$

(graph can't copy) A company wants to increase the \(10 \%\) peroxide content of its product by adding pure peroxide (100\% peroxide). If x liters of pure peroxide are added to 500 liters of its \(10 \%\) solution, the concentration, \(C,\) of the new mixture is given by $$ c=\frac{x+0.1(500)}{x+500} $$ How many liters of pure peroxide should be added to produce a new product that is \(28 \%\) peroxide?

A basketball player's hang time is the time spent in the air when shooting a basket. The formula \(t-\frac{\sqrt{d}}{2}\) models hang time, \(t\), in seconds, in terms of the vertical distance of \(a\) player's jump, \(d,\) in feet. When Michael Wilson of the Harlem Globetrotters slamdunked a basketball, his hang time for the shot was approximately 1.16 seconds. What was the vertical distance of his jump, rounded to the nearest tenth of a foot?