Chapter 3

Write an inequality describing the given quantity. Example: An MP3 player can hold up to 120 songs. Solution: The number of songs is \(n\) where \(0 \leq n \leq 120, n\) an integer. Chain can be purchased in one-inch lengths from one inch to twenty feet.

Are there values of \(x\) which satisfy the statements? Explain how you can tell without finding, or attempting to find, the values. $$ |x|-3=10 $$

Solve the equations in Exercises \(1-14\). \(0.5 x-3=11\)

Solve the equations. $$ 0.5 x-3=11 $$

Solve the equations. $$ \frac{5}{3}(y+4)=\frac{1}{2}-y $$

Write an inequality describing the given quantity. Example: An MP3 player can hold up to 120 songs. Solution: The number of songs is \(n\) where \(0 \leq n \leq 120, n\) an integer. Water is a liquid above \(32^{\circ} \mathrm{F}\) and below \(212^{\circ} \mathrm{F}\).

Are there values of \(x\) which satisfy the statements? Explain how you can tell without finding, or attempting to find, the values. $$ |x-3|=10 $$

Write an inequality describing the given quantity. Example: An MP3 player can hold up to 120 songs. Solution: The number of songs is \(n\) where \(0 \leq n \leq 120, n\) an integer. A 200 -gallon holding tank fills automatically when its level drops to 30 gallons.

Solve the equations. $$ 2(a+3)=10 $$

Write an inequality describing the given quantity. Example: An MP3 player can hold up to 120 songs. Solution: The number of songs is \(n\) where \(0 \leq n \leq 120, n\) an integer. Normal resting heart rate ranges from 40 to 100 beats per minute.

Solve the equations. $$ -9+10 r=-3 r $$

Are there values of \(x\) which satisfy the statements? Explain how you can tell without finding, or attempting to find, the values. $$ |2 x+5|=|-7-10| $$

Write an inequality describing the given quantity. Example: An MP3 player can hold up to 120 songs. Solution: The number of songs is \(n\) where \(0 \leq n \leq 120, n\) an integer. Minimum class size at a certain school is 16 students, and state law requires fewer than 24 students per class.

Solve the equations. $$ 4 p-1.3=-6 p-16.7 $$

Are there values of \(x\) which satisfy the statements? Explain how you can tell without finding, or attempting to find, the values. $$ |x-1|>2 $$

Write an inequality describing the given quantity. Example: An MP3 player can hold up to 120 songs. Solution: The number of songs is \(n\) where $0 \leq n \leq 120, n$ an integer. An insurance policy covers losses of more than \(\$ 1000\) but not more than $\$ 20,000$.

Are there values of \(x\) which satisfy the statements? Explain how you can tell without finding, or attempting to find, the values. $$ |3-x|-1<0 $$

Each of the inequalities can be solved by performing a single operation on both sides. State the operation, indicating whether or not the inequality changes direction. Solve the inequality. $$ 12 x \geq 60 $$

Solve the equations. $$ 0.2(g-6)=0.6(g-4) $$

Each of the inequalities can be solved by performing a single operation on both sides. State the operation, indicating whether or not the inequality changes direction. Solve the inequality. $$ -5 t<17.5 $$

Interpret each of the following absolute values as a distance on the number line. Evaluate when possible. (a) |3.5| (b) |-14| (c) \(|7-2|\) (d) \(|-7-2|\) (e) \(|x-4|\) (f) \(|x+4|\)

Solve the equations. $$ -4(2 m-5)=5 $$

Each of the inequalities can be solved by performing a single operation on both sides. State the operation, indicating whether or not the inequality changes direction. Solve the inequality. $$ -4.1+c \leq 2.3 $$

Classify each statement as true or false. (a) \(|-25|<0\) (b) \(-|-11|=11\) (c) \(|5-7|=|5|-|7|\) (d) \(|12-11|=|11-12|\) (e) \(\quad\) If \(x

Solve the equations. $$ 5=\frac{1}{3}(t-6) $$

Each of the inequalities can be solved by performing a single operation on both sides. State the operation, indicating whether or not the inequality changes direction. Solve the inequality. $$ -15.03>s+11.4 $$

Write an absolute value equation or inequality to describe each of the following situations. (a) The distance between \(x\) and zero is exactly 7 . (b) The distance between \(x\) and 2 is exactly 6 . (c) The distance between \(t\) and -2 is exactly 1 . (d) The distance between \(x\) and zero is less than 4 . (e) The distance between \(z\) and zero is greater than or equal to \(9 .\) (f) The distance between \(w\) and -5 is greater than 7 .

Solve the equations. $$ \frac{2}{3}(3 n-12)=\frac{3}{4}(4 n-3) $$

Each of the inequalities can be solved by performing a single operation on both sides. State the operation, indicating whether or not the inequality changes direction. Solve the inequality. $$ \frac{-3 P}{7}<\frac{6}{14} $$

Solve the absolute value equation by writing it as two separate equations. $$ |x-1|=6 $$

Solve the equations. $$ 3 d-\frac{1}{2}(2 d-4)=-\frac{5}{4}(d+4) $$

Each of the inequalities can be solved by performing a single operation on both sides. State the operation, indicating whether or not the inequality changes direction. Solve the inequality. $$ 27>-m $$

Solve the absolute value equation by writing it as two separate equations. $$ 5=|2 x|-3 $$

Solve the equations. $$ B-4(B-3(1-B))=57 $$

Each of the inequalities can be solved by performing two operations on both sides. State the operations in order of use and solve the inequality. $$ 5 y+7 \leq 22 $$

Solve the absolute value equation by writing it as two separate equations. $$ |2 t-1|=3 $$

Solve the equations. $$ 1.06 s-0.01(240-s)=22.67 s $$

Each of the inequalities can be solved by performing two operations on both sides. State the operations in order of use and solve the inequality. $$ -2(n-3)>12 $$

Solve the absolute value equation by writing it as two separate equations. $$ \left|2-\frac{r}{3}\right|=7 $$

Solve the equations in Exercises \(15-25 .\) $$ \frac{3}{z-2}=\frac{2}{z-3} $$

Each of the inequalities can be solved by performing two operations on both sides. State the operations in order of use and solve the inequality. $$ 13 \leq 25-3 a $$

Solve the absolute value equation by writing it as two separate equations. $$ 2=\frac{|p+1|}{4} $$

Solve the equations. $$ \frac{2}{2-x}-\frac{3}{x-5}=0 $$

Each of the inequalities can be solved by performing two operations on both sides. State the operations in order of use and solve the inequality. $$ 3.7-v \leq 5.3 $$

Solve the inequality. $$ |5+2 w|<7 $$

Solve the equations. $$ \frac{3}{2 x-1}+\frac{5}{3-2 x}=0 $$

Each of the inequalities can be solved by performing two operations on both sides. State the operations in order of use and solve the inequality. $$ \frac{5}{2} r-r<6 $$

Solve the inequality. $$ \left|\frac{x}{3}+7\right| \geq 2 $$

Solve the equations. $$ \frac{-3}{x-2}-\frac{2}{x-3}=0 $$

Each of the inequalities can be solved by performing two operations on both sides. State the operations in order of use and solve the inequality. $$ \frac{4}{3} x \geq 2 x-3 $$