# Basic Algebra Review

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Basic Algebra Review                                                 9. Given  ABC where m C  900 , AC  3,
and BC  4 . Find the measure of AB .
1. What is the value of x in the equation
2(x − 3) + 1 = 19?                                              10. Solve. 4x 2  36  0

                          
a) 6        b) 9    c) 10.5     d) 12                                                   

11. Christi and Laura start a lawn-mowing
2. What is the solution for the equation                               business and buy a lawnmower for \$225.
5(x + 1) = 5x + 2?                                                    They plan to charge \$15 to mow one lawn.
1                                                    What is the minimum number of lawns they
a) −1     b)          c) all real #       d) no sol
2                                                    need to mow if they wish to earn a profit of at
least \$750?
3. When 5 is divided by a number, the result is 3
more than 7 divided by twice the number. What

is the number?                                                    12. The formula for converting temperatures in
1
a) 1        b) 2        c)           d) 5                        degrees Celsius to degrees Fahrenheit is
2                                         9 
F   C  32 .   If the temperature is 200 C,
5 
4. Mr. Linnens has \$75 to spend on pizzas and
what is the temperature in degrees
soda pop. Pizzas cost \$9 each and drinks cost
                                                       Fahrenheit?
\$0.75 each. Five times as many drinks as                                                           
                a) 68 b) 43.1 c) 33.8 d) 4
pizzas are needed. What is the maximum
number of pizzas that Mr. Linnens can buy?
13. The expression x 2 16 is equivalent to
a) x  2x  8   b) x  2x  8
5. Give the statements: “t is a multiple of 3” and “t”
is even”. What could be a value of t?                                 c) x  4x  4   d) x  8x  8

a) 8    b) 9    c) 15      d) 24
                         
 14.     The width, w, of a rectangular rug is 4 less

6. The table shows the GPS coordinates of four                             than its length, l. Which expression
cities.                                                                 represents the area of the rug?
Chicago        (5985, 3439)                                        a) l 4  l          b) l l  4
Denver         (7490, 5881)                                        c) 2l  4  2l      d) 2w  2l
Huston         (8936, 3542)
Boston         (4422, 1241)                                                        

Find the distance between Boston & Denver.                         15. Simplify the expression 6  35x  2 10x .

a) 25x b) 8  25x c) 5x  6 d) 12  25x

7. Which equation is equal to 3x  4 y  15?
15 3x                                                                
        
 16. Ms. Lucero bought a refrigerator that cost
a) y                            b) y  15 3x
4                                                       \$1200, including tax. The cost of electricity to
3x 15                                                      run this refrigerator is estimated at \$78 per
c) y                            d) y  3x  15
4                                                      year. Which equation best represents c, the
                                                                       total cost of the refrigerator including electricity
over n years of operation?
8.
 Which equation illustrates the associative
                                                       a) c = 1200(78n)         b) c = 1200(n + 78)
property?                                                                  c) c = 1200 − 78n        d) c = 1200 + 78n
a) a  b  b  a        b) a  b  c  a  b  c
c) ab  c  ab  ac     d) a1  a                            17. Twenty-two is two less than six times a
number. Find the number.
                       
                               
18. The midpoint of TS is the origin and point T is      30. The length of a rectangle is nine and the width
located in Quadrant II. What quadrant                    is (x + 6). Find the value of x if the area of the
contains point S?                                        rectangle is 135 cm2. (A = l w)

19. Two cyclists start from the same point and ride      31. Lee, Kelly, Linda, and Madison all took the
in opposite directions traveling at the same             same math test. Linda earned a lower score
speed. In 3 hours they are 72 miles apart.               than Kelly, but she did not earn the lowest
Find the rate of each cyclist.                           score. The highest test-scorer’s name does not
begin with an L. Madison earned a higher
20. The sum of three consecutive even integers is            score than Kelly. Which person earned the
forty-two. Find the integers.                            lowest score on the math test?

21. A coin purse contains 16 coins in nickels and
dimes. The coins have a total value of \$1.           32. The pattern of dots shown below continues
Find the number of each type of coin in the              infinitely, with more dots being added at each
purse.                                                   step. Which expression can be used to
determine the number of dots in the nth step?
22. Scientists find that the height of a person, h, in
centimeters, is related to the length of the
person’s femur bone, f, in centimeters,
according to the formula h  69.09  2.24 f
What is the height of a person with a femur
bone of 48.6 cm in length?                                   a) 2n                  b) n(n + 2)
c) n(n + 1)            d) 2(n + 1)

23. One hose can fill a pool in 15 hours. A second
hose can fill a pool in 10 hours. How long
would it take to fill the pool using both hoses?     33. Which of the following expressions is equal to
the area of the shaded region in square units in
the diagram shown below?
24. A ship travels from Long Beach to the
Jiaozhou Gulf, a distance of 7200 miles. If the
ship travels at a rate of 480 miles per day,
how long will the trip take?

25. Brycen doubles his favorite number and adds 7
to get 21. What is Brycen’s number?
a) 5x2 + 4x - 2            b) 5x2 + 6x - 2
27. Pennie Pinches adds 5 dollars a week to her              c) 9x2 + 6x - 2            d) 7x2 + 5x - 2
balance of \$144. Write an equation that models
this situation. In how many weeks will she
have \$179?                                           34. Which algebraic expression best represents
the relationship between the terms in the
28. When twice a number is decreased by 3, the               following sequence and their position, n, in the
result is 253. What is the number?                       sequence?
0, 6, 16, 30, 48 …

29. The sides of a triangle are (x + 3),                            a) n – 2              b) 2n2 - 2
(x + 4), and (x + 7). Find the length of the                    c) 2n - 2             d) n2 - 2
longest side if the perimeter of the triangle is
104 inches.

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