Test #2, Review Solutions.
1. 5(3y – 2) = (4y + 4) + 2y
15y – 10 = 6y + 4
9y = 14
2.
3.
2x - 7 = 1
2x – 7 = 1
2x = 8
x=4
4.
h  16t 2  v0t
v0t  h  16t 2
6.
7.
14
9
x
19
3
x 7 5 x

2
4
x

7


 5 x 

4  
4
 2 
 4 
2(x – 7) = 5 – x
2x – 14 = 5 – x
3x = 19
5.
y
split into two problems
2x – 7 = -1
2x = 6
x=3
v0 
h  16t 2
t
Add the two distances
d1  rt
d2  r2t
1
d  rt
1  r2t
4
 4
4
1 hr 20 minutes =   hr
d  90    95  
3
 3
3
2
d = 120 miles + 126 miles
3
2
d = 246 miles
3
I = PRT
Jake
Rose
I = 5000 ( .0325)(1)
I = 5000(.0495)(1)
I = 162.50
I = 247.50
Difference 247.50 – 162.50 = 85.00
-8 < 3x – 5  16
-3 < 3x  21
-1 < x  7
(-1, 7]
add 5 to all three sides
divide all three sides by 3
put in interval notation
divide by –5 (Don’t forget to switch the sign)
split into two problems
3 + t > -2
t > -5
(-5, -1)
8.
-53 + t > -10
3 + t < 2
3+t<2
t < -1
9..
550 +80 + 420 + 250 + 80 + x < 1800
1380 + x < 1800
10.
11.
12.
(x – 3)2 = 12
x2 – 6x + 9 = 12
x2 – 6x – 3 = 0
6  36  4(1)(3)
2
6  48 6  (16)(3)
=
=
2
2
OR
(x – 3)2 = 12
x – 3 =  12
3 2 3
14.
multiply out (x – 3)2
set equal to zero
solve, it can’t be factored
64 3
2
=
1
h   (32)t 2  vot  ho
2
1
0   (32)t 2  83t  0
2
(x2 + 2)2 – 7(x2 + 2) + 12 = 0
w2 – 7w + 12 = 0
(w – 3)(w – 4) = 0
w=3 w=4
x2 + 2 = 3
x2 + 2 = 4
x  1,  1, 2,  2
x3 – 4x2 –2x + 8 = 0
x2(x – 4) – 2(x – 4) = 0
(x – 4)(x2 – 2) = 0
x  4, 2,  2
3 2 3
Square root each side
2x2 + 7x = x2 +2x -6
x2 + 5x + 6 = 0
(x + 2)(x + 3) = 0
0 = t(-16t + 83)
13.
x < 420
x = -2, -3
0 = -16t2 + 83t
t  0 or
83
16
Let w = x2 + 2
x2 = 1
x2 = 2
15.
16.
17.
18.
19.
20.
2 z 2  8 z  42
z 3
2( z  3)( z  7)
z 3
2( z 2  4 z  21)
z 3
2(z – 7) z  -3
3a 3  a
5a  1
3a3  5 a  5

5a  1 5a  1
y 3  6 y 2  17 y  2
7 y 2  15 y  2
x  x  3 3
x 3
x2 9



 
 
3 x  x  3
3 x
3x 3x
3
3 x
3 x
 1

  1 
x
x x
x x
x2  9
x
( x  3)( x  3)
x
( x  3)


3x 3  x
3x
3  x
3
x2  9
3x
3  x
x
x  0 or 3
y
1
y2
y
1
y2

 2


y 1 y  4 y  5 y  4
y  1 y  4 ( y  1)( y  4)
2
y( y  1)( y  4) 1( y  1)( y  4) y ( y  1)( y  4)


y 1
y4
( y  1)( y  4)
2
y2 –4y +y – 1 = y2
y( y  4)  ( y  1)  y
-3y - 1 = 0
y = -1/3
1 1
t  t 1
3 4
1(12) 1(12)
t
t  1(12)
3
4
12
7t = 12
t  hr
7
4t  3t  12
21.
or
a(3a 2  1)
5a  1
5x  1  4  x  1
( 5x  1)2  (4  x  1)2
5x  1  16  4 x  1  4 x  1  ( x  1)
5x  1  15  x  8 x  1
4 x  16  8 x  1
x  4  2 x  1
x2 – 8x + 16 = 4(x – 1)
x2 – 12x + 20 = 0
(x – 10)(x – 2) = 0
x = 2, 10
but 10 does not work
x = 2 only!
1
22.
1
 2 x  5 6   x  2  6
6
1
1

 

  2 x  5 6     x  2  6 

 

6
2x – 5 = x – 2
23.
 2x2 18x  67 
x = 3 This does check!
1
3
3
3
2x2 – 18x + 67 = 27
x2 – 9x + 20 = 0
 2 x 2  18 x  67 13   33
 


2x2 – 18x + 40 = 0
(x – 4)(x – 5) = 0
x = 4, 5
Reminder notes
1.5 – 1.8
 Separate absolute value problems into two equations after isolating the absolute
value side.
o Remember the absolute value can never be negative
o Use the same procedure if absolute value is on both sides of equal sign
 Know how to use distance and simple interest formulas
o Rate needs to be changed to a decimal by moving decimal twice to the left
o Time needs to be in years
 Solve single variable equations
o Be aware of special situations where all variable cancel out
 Remember to switch the inequality sign when you multiply or divide by a
negative number
 Separate absolute value inequalities into two inequalities
o One the same, the other switch the inequality sign and make the opposite
side negative
 Solving quadratic equations
o Factoring, perfect squares, quadratic formula
o Substitute w in for quadratic like equations
 Simplify rational expressions
o Must be multiplication
x7
o
 1
7x
o List out any value for x that would make denominator equal zero at any
time
o Get a common denominator when adding or subtracting
o Multiply by the reciprocal when dividing
o Take complex rational expressions one step at a time
 Get common denominators for top and bottom
 Multiply by the reciprocal
 Solve rational equations
o Multiply everything by the common denominator
o Check your answer to make sure it doesn’t make the denominator 0
 Know how to solve work problems when looking for total time or one rate
 Solve radical equations
o Check your answers if you take each side to a even power
o FOIL when squaring a binomial!!!!