MB32 – Test 1 Review Sheet Answers -4 0 4 6 -2 -2 6

MB32 – Test 1 Review Sheet Answers
1. Solve and check: 3 x+ (2x− 5) = 13− 2( x+
2)
3x+ 2x− 5= 13−2x−4
5x− 5= 9−2x
7x
= 14
x = 2
Name KEY
Check
3 x+ (2x− 5) = 13− 2( x+
2)
( ) + ( ) − = − ( + )
6+ 4− 5= 13−2( 4)
32 22 5 13 22 2
5=
5
2. Solve and graph:
a) 4−5( y −2) ≤−2( − 9+ 2 y)
e) 4x− 2 = 3x+
2
Case I
4 − 5y+ 10 ≤18 −4y
4x− 2= 3x+
2
14 ≤ 18 + y
x = 4
−4 ≤ y or y≥−4
Case II
− 4x
− 2 = 3x
+ 2
( )
− 4x
+ 2= 3x
+ 2
− 7x
= 0
x = 0
-4 0 4
b) y − 3 =− 3
f) 6x− 8 = 5x−
2
Case I Case II Case I Case II
−
( )
( 6x
− 8)
= 5x
−2
− y − 3 =−3
y − 3=−3
6x− 8= 5x−2
− 6x
+ 8= 5x
−2
− y + 3=−3
y = 0
6x= 5x+
6
10 = 11x
− y =−6
reject
x = 6
10
y = 6
x =
11
reject
No Solution
c) 2+ 3x
≥ 4
g) 1 4− 2y
> 4 First multiply by 2: 4− 2y
> 8
2
Case I Case II Case I Case II
− ( 2+ 3x)
≥4
−( 4− 2y)
> 8
2+ 3x
≥4
4− 2y
> 8
−2−3x
≥4
4− 2y
4
−3x
≥6
− 2y
6
10
11
6
-2
2
-2 6
3

d) y + 2 < 6
h) 5− 3(2x
+ 1) ≥ 2
Case I Case II Case I Case II
−[ 5− 3(2x
+ 1) ] ≥2
5− 3(2x
+ 1) ≥2
5− 3(2x
+ 1) ≤−2
− ( y + 2)
< 6
5− 6x
−3≥2
y + 2<
6
5− 6x
−3≤−2
y + 2>−6
2−
6x
≥ 2
y < 4
2−
6x
≤−2
y >−8
−6x
≥ 0
−6x
≤−4
x ≤ 0
2
x ≥
3
-8 4
0
2
3
3. The inequality − 3< x < 7 is the solution set of which of the following:
a) x − 2 > 5
b) x − 2 < 5 c) x + 2 > 5
d) x + 2 < 5
Solution set would be: Solution set would be: Solution set would be: Solution set would be:
x 7 − 3< x < 7
x< −7 ∨ x> 3
− 7< x < 3
4. Which of the following is the graph of the solution set of 15 < 3x
+ 5 < 21
a) b) c) d)
15 < 3x
+ 5 < 21
10 < 3x
< 16
10 16
< x <
3 3
1 1
3 < x < 5
3 3
5. Simplify (multiply, divide or combine):
a)
3 2 2 3 4 7
( − 2 x) (3 x ) = ( − 8 x )(9 x ) =− 72x
f)
2 3b 2b b
− 5 y ( y + y − y ) =
b)
2 x 3 x x 5 x 3 x
5 a (2 a − a ) = 10a − 5a
3b+ 2 2b+ 2 b+
2
−5y − 5y + 5y
c)
2 2
(3x+ 4) = 9x + 24x+ 16
g)
3
(2x − 3x+ 4)(2x+ 1) =
4 3 2
4x + 2x − 6x + 5x+
4
d)
a b 2 2a a b 2b
( x + y ) = x + 2x y + y
h)
4 4 3 3
13 abc÷ 13ab = abc
e)
2 2
+ − x− = 2 2
( x 3) ( 4)
x + 6x+ 9 −( x − 8x+ 16) = 14x− 7 i)
2a+ 4 3a+ 5 2a+ 1 3 a+
4
( −9x − 3 x ) ÷ ( − 3 x ) = 3x + x

6. Divide:
2
1
a) 6x − 13x+ 7 by 3x− 2=
2 x − 3 + 3 x − 2
2x − 3
2
b)
3 2 1
4 x + 7 x+ 3 by 2 x+ 1 = 2 x − x+ 4 − 2 x + 1
2
2x
− x + 4
3 2
3x − 2 6x
− 13x+ 7
2x + 1 4x + 0x + 7x+
3
2
−(6x
− 4 x)
3 2
− (4x
+ 2 x )
− 9x
+ 7
2
− 2x
+ 7x
−− ( 9x
+ 6)
2
−( −2 x − x)
1 8x + 3
− (8x
+ 4)
− 1