Download Solve for y: 3x 4y = 12

MATD 0390
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
(COVERS EII.B, EII.C, EII.E, EII.F, and 4.3)
x2 – y2
1.
Evaluate for x = –5 and y = 6:
2.
Evaluate for a = –2 and b = –3:
3.
Evaluate for w = –7, x = –6, and y = 2:
4.
Simplify:
(18z5 – 10xz4 – 5z – 14) + (9xz4 – z + 8)
5.
Simplify:
(5x3 + 13x2 – 7y – 2) – (4x3 + y – 6)
6.
Simplify:
(3a + 7b)(2a – 5b)
7.
Simplify:
(2x – 3)(x2 + 5x – 6)
8.
Simplify:
(5m – 4)2
9.
Solve for p: –3(p – 4) = 6
10.
Solve for s: 4s – 7 = –2(1 – s)
11.
Solve for y:
6
y = 12
7
12.
Solve for r:
4
(r – 10) = r + 2
5
13.
Solve for a:
14.
Solve for m:
2(2 + m) = 2m + 5
15.
Solve for x:
2
4
4
(x + 2) = x +
3
6
3
16.
Solve for y:
3x – 4y = 12
17.
Solve for c:
m = 5c – 7
18.
Solve for b:
1
N = bw
6
19.
Solve, write your answer in interval notation, and graph your solution on a number line:
2x ≤ –24
20.
Solve, write your answer in interval notation, and graph your solution on a number line:
x+8>3
21.
Solve, write your answer in interval notation, and graph your solution on a number line:
3x + 4 ≤ 5(x – 2)
(4a – b)2 – 5a3
xy – 3xy4 – 5w
1
2
(3a + 1) = (11 – a)
4
3
MATD 0390
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
PAGE 2
22.
Solve, write your answer in interval notation, and graph your solution on a number line:
–9 ≤ 3 – 2x < 18
23.
Solve for y:
|3y – 2| = |5y + 8|
24.
Solve for w:
3|w – 5| + 6 = 24
25.
Solve, write your answer in interval notation, and graph your solution on a number line: |x| ≥ 8
26.
Solve, write your answer in interval notation, and graph your solution on a number line: |a| < 5
27.
Factor completely:
24x5y3 + 36y7 – 30x2y8
28.
Factor completely:
25x3 – 36x
29.
Factor completely:
4x4 – 64
30.
Factor completely:
x2 + 25
31.
Factor completely:
2ac – 10bc – 3a + 15b
32.
Factor completely:
x5 – 27x2
33.
Factor completely:
a3b + 8b – 5a3 – 40
34.
Factor completely:
x2 + 5x – 6
35.
Factor completely:
x2 – 5x – 6
36.
Factor completely:
x2 – 5x + 6
37.
Factor completely:
x2 + 8x + 9
38.
Factor completely:
3x2 + 2xy – 8y2
39.
Factor completely:
5x2 – 32x + 12
40.
Factor completely:
2x5 – 10x3 – 72x
41.
Find the distance and midpoint between the points (–5, 2) and (1, –6).
42.
Find the distance and midpoint between the points (–3, –1) and (–4, 9).
43.
Find the slope and y-intercept of the line 5x – 4y = 12.
44.
Find the equation of the horizontal line and the equation of the vertical line that
pass through the point (–2, 7), and indicate the slope of each.
MATD 0390
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
PAGE 3
45.
(a) Graph x – 2y = –4, and
(b) indicate its slope.
46.
(a) Graph 3x + y = 5, and
(b) indicate its slope.
47.
(a) Graph 2x – 3 = 4, and
(b) indicate its slope.
48.
(a) Graph y = –6, and
(b) indicate its slope.
49.
Without graphing, determine whether the graphs of the equations below are parallel,
perpendicular, or neither.
3x + 9y = 36
y = 3x – 5
50.
Without graphing, determine whether the graphs of the equations below are parallel,
perpendicular, or neither.
10x + 2y = –8
y = –5x + 3
51.
Without graphing, determine whether the graphs of the equations below are parallel,
perpendicular, or neither.
x – 2y = 3
6x – 3y = 9
52.
For the line through the points (1, –5) and (–3, –7),
(a) find the slope, and
(b) find the equation of the line. Write your answer in slope-intercept form.
53.
Find the equation of the line through the point (–4, 5) and parallel to the line
x + 2y = 8. Write your answer in slope-intercept form.
54.
Find the equation of the line through the point (6, –1) and perpendicular to the line
3
y = – x + 4. Write your answer in slope-intercept form.
2
55.
Find the x-intercept and y-intercept of the line 2x – 3y = 8, and graph the line.
56.
Graph the inequality x + y ≤ –5.
57.
Graph the inequality 2x – y < 4.
58.
Graph the inequality 1 x + y < 3.
2
MATD 0390
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
PAGE 4
ANSWERS:
1.
–11
2.
65
3.
311
4.
18z5 – xz4 – 6z – 6
5.
x3 + 13x2 – 8y + 4
6.
6a2 – ab – 35b2
7.
2x3 + 7x2 – 27x + 18
8.
25m2 – 40m + 16
9.
p=2
10.
s=
11.
y = 14
12.
r = –50
13.
a=5
14.
No Solution
15.
All Real Numbers
16.
y=
3
x – 3
4
17.
c=
m+7
5
18.
b=
6N
w
19.
x ≤ –12
(–∞, –12]
The graph is a number line with a closed (meaning filled-in) circle at –12 with shading from –12
toward negative infinity (to the left). [Please refer to extra handout Exercise Set EII.C posted
at http://www2.austin.cc.tx.us/jbickham/handouts.]
5
2
MATD 0390
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
PAGE 5
ANSWERS:
20.
x > –5
(–5, ∞)
The graph is a number line with an open (meaning NOT filled-in) circle at –5 with
shading from –5 toward positive infinity (to the right). [Please refer to extra handout Exercise
Set EII.C posted at http://www2.austin.cc.tx.us/jbickham/handouts.]
21.
x ≥7
[7, ∞)
The graph is a number line with a closed (meaning filled-in) circle at 7 with
shading from 7 toward positive infinity (to the right). [Please refer to extra handout Exercise
Set EII.C posted at http://www2.austin.cc.tx.us/jbickham/handouts.]
22.
–
23.
y = –5 or y = –
24.
w = –1 or w = 11
25.
x ≤ –8 or x ≥ 8
(–∞, –8] U [8, ∞)
The graph is a number line with a closed (meaning filled-in) circle at –8 with shading from –8
toward negative infinity (to the left) and with another closed circle at 8 with shading from 8
toward positive infinity (to the right). There is no shading between –8 and 8. [Please refer to
extra handout Exercise Set EII.C posted at http://www2.austin.cc.tx.us/jbickham/handouts.]
26.
–5 < a < 5
(–5, 5)
The graph is a number line with open (meaning NOT filled-in) circles at both –5 and 5 with
shading between –5 and 5. [Please refer to extra handout Exercise Set EII.C posted at
http://www2.austin.cc.tx.us/jbickham/handouts.]
27.
6y3(4x5 + 6y4 – 5x2y5)
28.
x(5x + 6)(5x – 6)
29.
4(x + 2)(x – 2)(x2 + 4)
30.
PRIME (Not Factorable): Sum of Squares
31.
(a – 5b)(2c – 3)
15
< x ≤ 6
2
15
(–
, 6]
2
The graph is a number line with an open (meaning NOT filled-in) circle at –7.5, a closed
(meaning filled-in) circle at 6, and with shading between –7.5 and 6. [Please refer to extra
handout Exercise Set EII.C posted at http://www2.austin.cc.tx.us/jbickham/handouts.]
3
4
MATD 0390
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
PAGE 6
ANSWERS:
32.
x2(x – 3)(x2 + 3x + 9)
33.
(b – 5)(a + 2)(a2 – 2a + 4)
34.
(x + 6)(x – 1)
35.
(x – 6)(x + 1)
36.
(x – 2)(x – 3)
37.
PRIME (Not Factorable)
38.
(3x – 4y)(x + 2y)
39.
(5x – 2)(x – 6)
40.
2x(x + 3)(x – 3)(x2 + 4)
41.
Distance is 10, and midpoint is (–2, –2). [Please refer to extra handout Exercise Set EII.E
posted at http://www2.austin.cc.tx.us/jbickham/handouts.]
42.
Distance is 101 ≈ 10.05, and midpoint is (–
43.
Slope is m =
44.
Equation of horizontal line is y = 7, and slope of any horizontal line is zero.
Equation of vertical line is x = –2, and slope of any vertical line is undefined.
45.
(a)
1
x – 2y = –4, or y = x + 2
2
(b)
Slope is
7
, 4) or (–3.5, 4). [Please refer to extra handout
2
Exercise Set EII.E posted at http://www2.austin.cc.tx.us/jbickham/handouts.]
5
, and y-intercept is (0, –3).
4
1
.
2
MATD 0390
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
ANSWERS:
46.
47.
(a)
3x + y = 5, or y = –3x + 5
(b)
Slope is –3.
(a)
(b)
48.
Slope of any vertical line is undefined.
(a)
(b)
Slope of any horizontal line is zero.
PAGE 7
MATD 0390
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
PAGE 8
ANSWERS:
1
and 3: negative reciprocals).
3
49.
Perpendicular (Slopes are –
50.
Parallel [Slopes are both –5, and y-intercepts are different (–4 and 3). Note that if the
slopes were the same and the y-intercepts were also the same, the two equations
would represent the same line.]
51.
Neither (Slopes are
52.
(a)
slope m =
(b)
y =
1
and 2: neither the same nor negative reciprocals).
2
1
2
1
11
x –
2
2
53.
1
y = –2x+3
54.
y =
55.
x-intercept is (4, 0)
2
x–5
3
y-intercept is (0, –
8
2
) or (0, –2 )
3
3
MATD 0390
ANSWERS:
56.
57.
58.
INTERMEDIATE ALGEBRA
TEST 1 REVIEW
PAGE 9