Chapter 1

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

In Exercises 59–94, solve each absolute value inequality. $$ 5>|4-x| $$

Solve equation 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.. $$y=x+\sqrt{x+5} \text { and } y=7$$

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

In Exercises 59–94, solve each absolute value inequality. $$ 2>|11-x| $$

Solve equation by the method of your choice. $$ 2 x^{2}=250 $$

Exercises \(87-89\) 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. $$y=x-\sqrt{x-2} \text { and } y=4$$

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

In Exercises 59–94, solve each absolute value inequality.. $$ 1<|2-3 x| $$

Solve equation by the method of your choice. $$ x^{2}-2 x=1 $$

Exercises \(87-89\) 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 equation. $$\left[(3+6)^{2} \div 3\right] \cdot 4=-54 x$$

In Exercises 59–94, solve each absolute value inequality. $$ 4<|2-x| $$

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

In Exercises 59–94, solve each absolute value inequality. $$ 12<\left|-2 x+\frac{6}{7}\right|+\frac{3}{7} $$

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

In Exercises 59–94, solve each absolute value inequality. $$ 1<\left|x-\frac{11}{3}\right|+\frac{7}{3} $$

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

In Exercises 59–94, solve each absolute value inequality. $$ 4+\left|3-\frac{x}{3}\right| \geq 9 $$

Solve equation by the method of your choice. $$ (3 x-4)^{2}=16 $$

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

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

In Exercises 59–94, solve each absolute value inequality. $$ \left|2-\frac{x}{2}\right|-1 \leq 1 $$

Solve equation by the method of your choice. $$ (2 x+7)^{2}=25 $$

Find all values of \(x\) satisfying the given conditions. $$y_{1}=6\left(\frac{2 x}{x-3}\right)^{2}, y_{2}=5\left(\frac{2 x}{x-3}\right), \text { and } y_{1} \text { exceeds } y_{2} \text { by } 6$$

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

Solve equation by the method of your choice. $$ 3 x^{2}-12 x+12=0 $$

Solve each equation. $$\left|x^{2}+2 x-36\right|=12$$

Solve each equation. $$4 x+13-\\{2 x-[4(x-3)-5]\\}=2(x-6)$$

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. $$ y_{1}=\frac{2}{3}(6 x-9)+4, y_{2}=5 x+1, \text { and } y_{1}>y_{2} $$

Solve equation by the method of your choice. $$ 9-6 x+x^{2}=0 $$

Solve each equation. $$\left|x^{2}+6 x+1\right|=8$$

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

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. \(y=1-(x+3)+2 x\) and \(y\) is at least 4

Solve equation by the method of your choice. $$ 4 x^{2}-16=0 $$

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

The data displayed by the bar graph can be described by the mathematical model $$p=\frac{4 x}{5}+25$$ where \(x\) is the number of years after 1980 and \(p\) is the percentage of U.S. college freshmen who had an average grade of \(A\) in high school. Use this information to solve Exercises \(97-98\) a. According to the formula, in \(2010,\) what percentage of U.S. college freshmen had an average grade of A in high school? Does this underestimate or overestimate the percent displayed by the bar graph? By how much? b. If trends shown by the formula continue, project when \(57 \%\) of U.S. college freshmen will have had an average grade of \(\mathrm{A}\) in high school.

In Exercises 95–102, use interval notation to represent all values of x satisfying the given conditions. \(y=2 x-11+3(x+2)\) and \(y\) is at most 0

Solve equation by the method of your choice. $$ 3 x^{2}-27=0 $$

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