Chapter 1

Solve each equation or formula for the specified variable. $$ d=r t, \text { for } r $$

Write expressions having values from one to ten using exactly four 4 \(\mathrm{s}\) . You may use any combination of the operation symbols \(+,-, \mathrm{x}, \div,\) and / or grouping symbols, but no other digits are allowed. An example of such an expression with a value of zero is \((4+4)-(4+4) .\)

Solve each inequality. Then graph the solution set on a number line. \(9 z+2>4 z+15\)

Simplify each expression. $$ 3(15 x-9 y)+5(4 y-x) $$

Solve each equation or formula for the specified variable. $$ x=\frac{-b}{2 a}, \text { for } a $$

Solve each equation. Check your solutions. \(3|p-5|=2 p\)

How to evaluate \(a+b[(c+d) \div e],\) if you were given the values for \(a, b, c, d,\) and \(e .\)

HEALTH Hypothermia and hyperthermia are similar words but have opposite meanings. Hypothermia is defined as a lowered body temperature. Hyperthermia means an extremely high body temperature. Both conditions are potentially dangerous and occur when a person's body temperature fluctuates by more than \(8^{\circ}\) from the normal body temperature of \(98.6^{\circ} \mathrm{F}\) . Write and solve an absolute value inequality to describe body temperatures that are considered potentially dangerous.

Solve each inequality. Then graph the solution set on a number line. \(2(g+4)<3 g-2(g-5)\)

Simplify each expression. $$ 2(10 m-7 a)+3(8 a-3 m) $$

Solve each equation or formula for the specified variable. $$ V=\frac{1}{3} \pi r^{2} h, \text { for } h $$

Solve each equation. Check your solutions. \(3|2 a+7|=3 a+12\)

MAIL For Exercises 40 and 41 , use the following information The U.S. Postal Service defines an oversized package as one for which the length \(L\) of its longest side plus the distance \(D\) around its thickest part is more than 108 inches and less than or equal to 130 inches. Write a compound inequality to describe this situation.

Solve each inequality. Then graph the solution set on a number line. \(3(a+4)-2(3 a+4) \leq 4 a-1\)

Simplify each expression. $$ 8(r+7 t)-4(13 t+5 r) $$

Solve each equation or formula for the specified variable. $$ A=\frac{1}{2} h(a+b), \text { for } b $$

Solve each equation. Check your solutions. \(|3 x-7|-5=-3\)

MAIL For Exercises 40 and 41 , use the following information The U.S. Postal Service defines an oversized package as one for which the length \(L\) of its longest side plus the distance \(D\) around its thickest part is more than 108 inches and less than or equal to 130 inches. If the distance around the thickest part of a package= you want to mail is 24 inches, describe the range of lengths that would classify your package as oversized.

Solve each inequality. Then graph the solution set on a number line. \(y<\frac{-y+2}{9}\)

Simplify each expression. $$ 4(14 c-10 d)-6(d+4 c) $$

If \(3 a+1=\frac{13}{3},\) what is the value of \(3 a-3 ?\)

Solve each equation. Check your solutions. \(16 t=4|3 t+8|\)

How many cubes that are 3 inches on each edge can be placed completely inside a box that is 9 inches long, 6 inches wide, and 27 inches tall? F. 12 G. 54 H. 36 J. 72

Solve each inequality. Then graph the solution set on a number line. \(\frac{1-4 p}{5}<0.2\)

Simplify each expression. $$ 4(0.2 m-0.3 n)-6(0.7 m-0.5 n) $$

Solve each equation. Check your solutions. \(-2 m+3=|15+m|\)

Evaluate each expression. \(\sqrt{9}\)

Solve each inequality. Then graph the solution set on a number line. \(\frac{4 x+2}{6}<\frac{2 x+1}{3}\)

Simplify each expression. $$ 7(0.2 p+0.3 q)+5(0.6 p-q) $$

For Exercises 42 and \(43,\) define a variable, write an equation, and solve the problem. GEOMETRY The perimeter of a regular octagon is 124 inches. Find the length of each side.

Evaluate each expression if \(x=6, y=2.8,\) and \(z=-5\). \(9-|-2 x+8|\)

Evaluate each expression. \(\sqrt{16}\)

GEOMETRY For Exercises 44 and \(45,\) use the following information. The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side. Write three inequalities to express the relationships among the sides of \(\triangle A B C .\)

Solve each inequality. Then graph the solution set on a number line. \(12\left(\frac{1}{4}-\frac{n}{3}\right) \leq-6 n\)

Write an algebraic expression to represent each verbal expression. the square of the quotient of a number and 4

Evaluate each expression if \(x=6, y=2.8,\) and \(z=-5\). \(3|z-10|+|2 z|\)

Evaluate each expression. \(\sqrt{100}\)

Mrs. Lucas earns a salary of \(\$ 34,000\) per year plus 1.5\(\%\) commission on her sales. If the average price of a car she sells is \(\$ 30,500\) , about how many cars must she sell to make an annual income of at least \(\$ 50,000 ?\) Write an inequality to describe this situation.

Write an algebraic expression to represent each verbal expression. the cube of the difference of a number and 7

Evaluate each expression if \(x=6, y=2.8,\) and \(z=-5\). \(|z-x|-|10 y-z|\)

Evaluate each expression. \(\sqrt{169}\)

For Exercises \(46-49,\) use the following information. You can use the operators in the LOGIC menu on the TI-83/84 Plus to graph compound and absolute value inequalities. To display the LOGIC menu, press 2nd Test. Clear the \(Y=\) list. Enter \((5 x+2 > 12)\) and \((3 x-8 < 1)\) as \(Y 1\) . With your calculator in DOT mode and using the standard viewing window, press GRAPH. Make a sketch of the graph displayed.

Mrs. Lucas earns a salary of \(\$ 34,000\) per year plus 1.5\(\%\) commission on her sales. If the average price of a car she sells is \(\$ 30,500\) , about how many cars must she sell to make an annual income of at least \(\$ 50,000 ?\) Solve the inequality and interpret the solution.

NUMBER THEORY For Exercises \(46-49,\) use the properties of real numbers to answer each question. If \(m+n=m,\) what is the value of \(n ?\)

GEOMETRY For Exercises 46 and \(47,\) use the following information. The formula for the surface area of a cylinder with radius \(r\) and height \(h\) is \(\pi\) times twice the product of the radius and height plus twice the product of \(\pi\) and the square of the radius. Write this as an algebraic expression.

A machine fills bags with about 16 ounces of sugar each. After the bags are filled, another machine weighs them. If the bag weighs 0.3 ounce more or less than the desired weight, the bag is rejected. Write an equation to find the heaviest and lightest bags the machine will approve.

Evaluate each expression. \(-\sqrt{4}\)

Define a variable and write an inequality for each problem. Then solve. Twice the sum of a number and 5 is no more than 3 times that same number increased by 11.

NUMBER THEORY For Exercises \(46-49,\) use the properties of real numbers to answer each question. If \(m+n=0,\) what is the value of \(n ?\) What is \(n^{\prime}\) s relationship to \(m ?\)

GEOMETRY For Exercises 46 and \(47,\) use the following information. The formula for the surface area of a cylinder with radius \(r\) and height \(h\) is \(\pi\) times twice the product of the radius and height plus twice the product of \(\pi\) and the square of the radius. Write an equivalent expression using the Distributive Property.