Chapter 1

Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. (graph cannot copy for a,b,c,d,e,f) $$y=2(x+2)^{2}+5(x+2)-3$$

At the north campus of a performing arts school, \(10 \%\) of the students are music majors. At the south campus, \(90 \%\) of the students are music majors. The campuses are merged into one east campus. If \(42 \%\) of the 1000 students at the east campus are music majors, how many students did the north and south campuses have before the merger?

Solve each equation in Exercises \(83-108\) by the method of your choice. $$ 5 x^{2}+2=11 x $$

Find all values of \(x\) satisfying the given conditions. $$y=|5-4 x| \text { and } y=11$$

Solve each absolute value inequality. $$3 \leq|2 x-1|$$

Evaluate \(x^{2}-x\) for the value of \(x\) satisfying \(4(x-2)+2=4 x-2(2-x)\).

The price of a dress is reduced by \(40 \% .\) When the dress still does not sell, it is reduced by \(40 \%\) of the reduced price. If the price of the dress after both reductions is \(\$ 72,\) what was the original price?

Solve each equation in Exercises \(83-108\) by the method of your choice. $$ 5 x^{2}=6-13 x $$

Find all values of \(x\) satisfying the given conditions. $$y=|2-3 x| \text { and } y=13$$

Solve each absolute value inequality. $$9 \leq|4 x+7|$$

Evaluate \(x^{2}-x\) for the value of \(x\) satisfying \(2(x-6)=3 x+2(2 x-1)\).

In a film, the actor Charles Coburn plays an elderly "uncle" character criticized for marrying a woman when he is 3 times her age. He wittily replies, "Ah, but in 20 years time I shall only be twice her age." How old is the "uncle" and the woman?

Solve each equation in Exercises \(83-108\) by the method of your choice. $$ 3 x^{2}=60 $$

Will help you prepare for the material covered in the next section. If 6 is substituted for \(x\) in the equation $$ 2(x-3)-17=13-3(x+2) $$ is the resulting statement true or false?

Find all values of \(x\) satisfying the given conditions. $$ y=x+\sqrt{x+5} \text { and } y=7 $$

Solve each absolute value inequality. $$5>|4-x|$$

Evaluate \(x^{2}-(x y-y)\) for \(x\) satisfying \(\frac{3(x+3)}{5}=2 x+6\) and \(y\) satisfying \(-2 y-10=5 y+18\).

Suppose that we agree to pay you 8e for every problem in this chapter that you solve correctly and fine you \(5 \phi\) 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. $$ 2 x^{2}=250 $$

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

Find all values of \(x\) satisfying the given conditions. $$ y=x-\sqrt{x-2} \text { and } y=4 $$

Solve each absolute value inequality. $$2>|11-x|$$

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

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

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

Find all values of \(x\) satisfying the given conditions. $$ y=2 x^{3}+x^{2}-8 x+2 \text { and } y=6 $$

Solve each absolute value inequality. $$1<|2-3 x|$$

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

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. $$ 2 x^{2}+3 x=1 $$

Find all values of \(x\) satisfying the given conditions. $$y=x^{3}+4 x^{2}-x+6 \text { and } y=10$$

Solve each absolute value inequality. $$4<|2-x|$$

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

$$\text { Solve for } C: \quad V=C-\frac{C-S}{L} N$$

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

Find all values of \(x\) satisfying the given conditions. $$y=(x+4)^{\frac{3}{2}} \text { and } y=8$$

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

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

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. $$ (2 x-5)(x+1)=2 $$

Find all values of \(x\) satisfying the given conditions. $$y=(x-5)^{\frac{3}{2}} \text { and } y=125$$

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

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

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. $$ (3 x-4)^{2}=16 $$

Find all values of \(x\) satisfying the given conditions. \(y_{1}=\left(x^{2}-1\right)^{2}, y_{2}=2\left(x^{2}-1\right),\) and \(y_{1}\) exceeds \(y_{2}\) by 3

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

Solve equation. \(0.7 x+0.4(20)=0.5(x+20)\)

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. $$ (2 x+7)^{2}=25 $$