91Ó°ÊÓ

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$4(x+1)+2 \geq 3 x+6$$

Solve each equation in by making an appropriate substitution. $$ 4 x^{4}=13 x^{2}-9 $$

Exercises \(31-50\) contain equations with variables in denominators. For each equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. $$ \frac{3}{x+2}+\frac{2}{x-2}=\frac{8}{(x+2)(x-2)} $$

Use the position formula $$ s=-16 t^{2}+v_{0} t+s_{0} $$ \(\left(v_{0}=\text { initial velocity, } s_{0}=\text { initial position, } t=\text { time }\right)\) to answer Exercises \(49-52 .\) If necessary, round answers to the nearest hundredth of a second. A projectile is fired straight upward from ground level with an initial velocity of 128 feet per second. During which interval of time will the projectile's height exceed 128 feet?

In Exercises \(51-58,\) determine whether each equation is an identity, a conditional equation, or an inconsistent equation. $$ \frac{2 x}{x-3}=\frac{6}{x-3}+4 $$

Solve each absolute value equation or indicate the equation has no solution. $$ |3 x-2|+4=4 $$

Solve each inequality by first rewriting each one as an equivalent inequality without absolute value bars. Graph the solution set on a number line. Express the solution set using interval notation. $$3|x-1|+2 \geq 8$$

What is the difference between solving an equation such as \(2(x-4)+5 x=34\) and simplifying an algebraic expression such as \(2(x-4)+5 x ?\) If there is a difference, which topic should be taught first? Why?

The Food Stamp Program is America's first line of defense against hunger for millions of families. Over half of all participants are children; one out of six is a low-income older adult. Exercises \(101-104\) involve the number of participants in the program from 1990 through 2000 . The formula $$ y=-\frac{1}{2} x^{2}+4 x+19 $$ models the number of people, \(y,\) in millions, receiving food stamps \(x\) years after \(1990 .\) Use the formula to solve Exercises 101-102 In which years did 19 million people receive food stamps?

The length of a rectangular garden is 5 feet greater than the width. The area of the garden is 300 square feet. Find the length and the width.