Exam 2: Equations, Inequalities, and Problem Solving

Write the algebraic expression described. Simplify if possible. -If x is the first of three consecutive integers, express the sum of 22 and the third integer as an algebraic expression in terms of x.

Simplify the expression. First use the distributive property to remove any parentheses. -6(x - 8)

Solve the inequality. Graph the solution set and write it in interval notation. - $2 \leq 2 ( x - 5 ) \leq 6$

Solve. -The sum of four times a number and three is the same as the difference of twice the number and eleven. Find the number.

Identify the numerical coefficient of the term. - $5 y$

Fill in the blank with one of the words or phrases listed below. -A(n) can be written in the form ax + b = c.

Solve. -A certain vehicle has a weight limit for all passengers and cargo of 1277 pounds. The four passengers in the vehicle weigh an average of 180 pounds. Use an inequality to find the maximum weight of the cargo that the vehicle can handle.

Simplify the expression. First use the distributive property to remove any parentheses. -9(y + 9)

Solve. -Melissa invested a sum of money at 3% annual simple interest. She invested three times that sum at 5% annual simple interest. If her total yearly interest from both investments was $3600, how much Was invested at 3%?

Simplify the expression by combining any like terms. -4x + 2x

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -The population of a town is currently 45,000. This represents an increase of 60% from the population 5 years ago. Find the population of the town 5 years ago. Round to the nearest whole Number if necessary.

Solve. -Center City East Parking Garage has a capacity of 257 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1221 cars, find the capacity for each garage.

Solve. -Professor Chang will give a student in her algebra class an A if his or her final score is at least 93 , a $\mathrm { B }$ if the score is between 84 and 92 , inclusive, and a $\mathrm { C }$ if the score is between 75 and 83 , inclusive. Any student with a score between 66 and 74, inclusive, will receive a D, and anyone with a score at or below 65 will fail with a grade of an F. Letting x represent a student's grade, write a series of five inequalities corresponding to the possible grades given in the class.

Graph the inequality on a number line. Then write the solution in interval notation. - $x \leq 1$

Simplify the expression. First use the distributive property to remove any parentheses. --(8y - 6z + 7)

Solve the equation. -4(x + 5) = (4x + 20)

Simplify the expression. First use the distributive property to remove any parentheses. -6(4x + 6y + 8)

Solve the equation. --10x = 0

Solve the equation. - $3 y - 7 + y = - ( y + 7 y )$

Solve. -A number increased by three-fourths of the number is 14. Find the number.