# Algebra Work

1) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.

2) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.

3) Solve the equation below. Show all work following the methods discussed in class; if an equation includes fractions, clear the fractions in the first step. If the equation has a unique solution, please show the complete check of your answer.

4) Solve the inequality below. Show all work following the methods discussed in class; if an inequality includes fractions, clear the fractions in the first step. Write your answer in interval notation and graph the solution set on a number line.

5) Solve the inequality below. Show all work following the methods discussed in class; if an inequality includes fractions, clear the fractions in the first step. Write your answer in interval notation and graph the solution set on a number line.

6) David wins \$800,000 (after taxes) in the lottery and decides to invest half of it in a 5-year CD that pays 5.32% interest compounded monthly. He invests the other half in a money market fund that unfortunately turns out to average only 3.4% interest compounded annually over the 5-year period. How much money will he have altogether in the two accounts at the end of the 5-year period?

7) The average annual tuition and fees at public 4-year institutions in the US in 2004 was \$13,576 and in 2014 was \$18,231. Let y be the average tuition and fees in the year x, where x = 0 represents the year 2004.

a) Write a linear equation that models the growth in average tuition and fees at public 4-year institutions in the US in terms of the year x.

b) Use this equation to predict the average tuition and fees at public 4-year institutions in the US in the year 2020.

c) Explain what the slope of this line means in the context of the problem.

8) Given the equation:

a) Rewrite the equation in slope-intercept form.

b) Write an equation in point-slope form of the line through the point (4, -5) perpendicular to the line with the equation given above.

c) Convert the equation found in part (b) to slope-intercept form.

d) Convert the equation found in part (c) to standard form, Ax + By = C, where A, B, and C are integers.

e) Graph both lines on one coordinate system. You may use the grid below, or attach your own. If you attach your own graph, please use graph paper with clearly labeled and scaled axes.

9) Show all work as you perform the indicated operations and simplify the result:

10) Show all work as you perform the indicated operations and simplify the result. Write the answer with positive exponents only.

11) Show all work as you perform the indicated operations and simplify the result. Start by clearing all parentheses.

12) Show all work as you multiply the polynomials and simplify the result:

371211

xx

-³+

20178

x

-£-<

4315

xy

-=

(

)

(

)

3

8253

27

xyxy

915

4

48

88

xy

xy

(

)

(

)

(

)

32232

12498275815

xxxxxxx

–+-+—

(

)

(

)

2

653412

xxx

-+-

(

)

(

)

4214621

xx

+-=-+

(

)

(

)

(

)

345342111

xxx

-+-=–

411292

33305

nnn

-=–

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