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Math 111
Solving Equations Review
Solve the equation both algebraically and graphically where possible.
x
4 x
 14
1. 3(2  x)   21 
4
2
2.
x x5

 2x  3
2
3
3. 5x – ( 2x + 14 ) = 10
4.
5x – 3(x+1) = 2(x+3) – 5
5. 7 – 4(x – 1) = x+1
5.
3x 1
 ( x  2)  10
2 4
7.
2(π + 3x) –
8. –1 – 2(3x – 5) = 3(3 – 2x)
9.
3( x  1)  x 2  2 x  1
10. x 2  x  42  0
11.
x 2  10  11x
12. t 2  4t  16
13.
2x( x – 5 ) = 12
14. 4 x 2  2 x  7
15.
5x
2
x 1
16. ( x + 3 ) ( 3 x + 5 ) = 7
17.
( x + 3 ) ( x – 2 ) = 50
18. 6 x 2  2 x  1
19.
x2  4x  7
20.
x4  x2
21.
x  7  x 1
22.
2x 1  2  x
23.
2x  8  4  0
6. A 
Math 111
h
(a  b) , solve for a
2
Equation Review
x
=
4
2x–5
2
page 1
3x  4  8
x2 5
25.
26. |3x – 4 | = 8
27.
|x+4|=5x–2
24.
28.
3x
1
3


x 9 x 3 x 3
29.
x
30.
1
2
x
 
x 1 x x 1
31.
8x
8
 4
x 1
x 1
32. 8x  2 x1
33.
5x  2
34. 24 x 1  31 x
35.
7 + 2 log(5x) = 11
36. ln ( x – 3 ) = 5 – ln ( x – 3 )
37.
log ( x – 16 ) = 2 – log ( x – 1 )
39.
10cos2 ( x)  3sin( x)  9  0
41.
ax + by = c, solve for y
1 1 1
 
, solve for s
r s t
43.
x2 + 96x − 2,304 = 0
44. 2.5x2 − 3.7x − 4.3 = 0
45.
25y2 = 49
46. 2Q(Q − 5) = 12
47.
48. x 2 / 3  2 x1/ 3  15  0
49.
2
38. cos( x ) 
3
; for all solutions, exactly
2
40. 5cos( x)  3cos(2 x)  3
42.
6
 5
x
5 x 2  2 x  3x
15, 000 
20, 000
1  24e  x / 4
50. log ( 3x + 2 ) + log ( x + 2 ) = log ( 7x + 6 )
Math 111
Equation Review
page 2