Download Objective #1

Algebra 1 Unit 2 Equations & Inequalities
Study Guide L3 2016-2017
Name_______________________________
Block________Date____________________
Do all problems, showing your work in the space provided. Be sure to show complete & proper work! This is due on the
day of the test, at the start of the block. Answers are posted on my website. You must show work to get credit.
Total: 48 Points
Objective #1 – Be able to solve and Check any equation in a single variable.
SOLVE THE FOLLOWING IN THE SPACE PROVIDED. Show a check on #s 4, 10 & 13
1) 26 – 9p = -1 _________________
3)
2)
y
+ 2 = 0 ___________________
4
4
c – 12 = -32 _______________
5
4) 17 = 5 – 3p _________________
5) -2( 4 - x) -7 = 5 ___________________
check of #4:
6) 9w + 24 = -3w ________________
7) 6r – 2 – 9r = 1 ____________
8) 16 = 5(1 – x) ________________
9)
2
(6 – 2a) = 6 _______________
3
10)
n – 4(1 + 5n) = 34 ___________
11)
12 – 4m = -18 + 11m ___________
Check of #10:
12) 9(-5 – x) = -10 – 2x ________________
13) -4y – (5y + 6) = -7y + 3 __________
Check #13
14) -3(x – 2) = x _________________
15)
1 5
2
3
 x  x  ______________
2 12
3
4
16) 24w – 8 – 10w = -2(4 – 7w) __________
17) 6m – 3 = 10 – 6( 2 – m) ___________
18) -3(-x – 4) = 2x + 1 ________________
19) -4(x – 3) = 6(x + 5) ___________
Thinking about solutions – answer these questions completely.
20) What are the three possible types of solutions you can have for an equation in a single variable? Answer completely
and specifically. Show an example for each.
Objective #2 – Solve any inequality, illustrate the solution set algebraically, with interval notation and graphically.
Solve each inequality. Show all work & graph the solution set on a number line graph. Write your solution in interval
notation also.
22) 5 x  10  35 or 25 – x < 4
23) x + 3  2(x – 4)
24) 3x + 2  7x
25) 12 > -2x – 6 > 2
26) 2x + 6 > 16 and 3x – 3 < 3
27) –3x – 1 < 2 or
8
2
x2
3
Objective #3 Use an Algebra Model (expressions & equations) to represent any real life problem.
Solve each problem using an ALGEBRA METHOD – show your equation and your solving work. If needed include a
picture. Answer the question with the appropriate labels or a sentence or an explanation.
28) The Great American Pizza Emporium charges a fixed rate of $8.35 for a cheese pizza. There is a charge of $1.35 for
each additional topping. Brittany and her friends ordered 3 pizzas, each with the same number of toppings. If their bill
was $37.20, how many additional toppings did they order on each pizza? Make an algebra model (equation) to
represent this problem – solve it and answer the question.
29) You have a container filled with coins, a mix of quarters and nickels. You find that the total value of coins is $106.
You determine that the number of nickels is thirty-six less than twice the number of quarters. How many of each coin do
you have?
30) Kirk has as many quarters as Gloria has dimes, as many dimes as Gloria has quarters, and as many nickels as Gloria
has. Neither has any other money. Gloria has 5 more dimes than nickels and 10 more quarters than dimes. Kirk has
$5.95. Write an equation for how much money Kirk has. Solve and found out how many of each coin each person has.
31) Mary needs to send a package to Maine. Federal Package Company charges a base fee of $8 plus an additional $2
per pound. United Shipping Service charges a base fee of $13 plus an additional $1 per pound. Which company is more
economical? Use Algebra to set up a model, showing solving steps and justify your answer completely and specifically!
32) The length of a rectangle is 3 more than the twice width. If the perimeter of the rectangle is 108 inches, find the
dimensions of the rectangle. Create an algebra model for this situation – solve it and answer the question.
Objective #4 – Be able to justify the process of simplifying algebraic expression using the properties learned in class.
33) Justify each step with properties!
Simplify 2(3x + 5) – 5(2 – x)
6x + 10 – 5(2 – x)
6x + 10 – 5(2 – 1x)
6x + 10 – 10 + 1x
6x + 1x + 10 – 10
7x + 10 – 10
7x + 0
7x
Objective #5 Solve any absolute value equation (and show understanding of what is meant by absolute value).
Solve each absolute value equation, use the graph method to help you visualize the distance from zero for any absolute
value part.
34) |x| = 3
35) 7|x| = 56
36) |2x – 5| = 17
37)
38) |3m| + 12 = 4
39) 9|3x + 6| + 3 = 30
4 |n – 8| = 56
Objective #6 Solve a formula for one of its variables, put an equation into function form (solve for y).
40) The volume of a rectangular prism is found with the formula V = LWH. Solve this formula for H.
41) The area of a trapezoid is given by the formula A 
h(a  b )
. Solve this formula for b.
2
42) Given the equation 3x + 5y = 20, put into function form (solve for y)
43) Given the equation 1 + 7y = 5x – 6, put into function form (solve for y)
44) Given the equation y + 5 = -2(x – 3) , put into function form, solve for y, clear parentheses)
45) The formula A = P + Prt is used to calculate interest and amount of money you have after interest is calculated.
a)
b)
Now use your new formula to solve this problem: