1. Solve for the variable. \(7 y + 3 ( 6 y - 11 ) = 167\).

2. Solve for the variable and place the final answer in interval notation. \(- 5 < - 2 x + 1 \leq 13\).

3. Break-even Analysis. A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copyediting, typesetting, and so on) at \( \$ 87,000 \) and variable costs (printing, paper, binding, shipping) at \( \$ 4.50 \) for each book produced. If the book is sold to distributors for \( \$ 28 \) each, how many must be produced and sold for the publisher to break even? 

4. Write the equation of the line in slope-intercept form with the given characteristics: 

a. Slope is \( - 5 \) and \( y \) -intercept is \( ( 0 , - 6 ) \) 

b. Slope is \( \frac { - 4 } { 5 } \) and passes through the point \( ( 2 , - 3 ) \) . 

c. Passes through the point \( ( 0,6 ) \) and \( ( 5,0 )\) 

5. Find the \( x \) -intercept and the \( y \) -intercept. 

a. \( y = \frac { 1 } { 2 } x - 1 \) 

b. \( y = \frac { 4 } { 3 } x - 4\) 

6. A new car worth \( \$ 45,000 \) is depreciating in value by \( \$ 5000 \) per year. 

a. Find the linear model for the current value of the car, \( v \) , and the number of years, \( y \) , after it was purchased. 

b. Interpret the slope of the model. 

c. If the car is \( 3 \) years old, what does the model predict for its value? 

d. After how many years will the car be worth nothing?