Linear Equations and Inequalities – Elementary Algebra
Solve:
1. 3(2t  1)  4(3t  2)
2. 3(n 10)  5(n  12)   86
3.
n 5n 1


3 6 8
Solve the inequality. Graph the solution set and write it in interval notation:
4. 7 x  8  5 x  38
5. 6 x  3  8 x  3
6. 6( x 1)  8( x  5)
3x
2
x


7.
5
3 10
8. Determine the slope and y –Intercept of 3x  5 y  15 .
9. Find the slope between (– 3, 5) and (– 2, 8)
10. Write the equation of the line that has a slope of
3
and contains the point  2,  4  .
5
Express the equation in the form Ax  By  C , where A, B, and C are integers.
11. Write the equation of the line that goes through 1, 4  and  9, 10 .
Express the equation in the form Ax  By  C , where A, B, and C are integers.
System of Equations
 3x  2 y  7 
12. Solve for x: 

 4x  5 y  3 
 2x  5 y  7 
13. Solve for y: 

 x  3y  1 
 x y 6 
14. Solve: 

 2x  2 y  5 
1


y  x  2

15. Solve for x:
3


x

3
y  6 

1
16. Solve for b : A  bh
2
17. Solve for L : P  2L  2W
18. Solve for x: 3x  4 y   7
19. Solve:
x 5
20. Solve:
x  2 1
Answers:
11
6
2. n 2
3
3. n 
28
4.   , 23
1. t 
)
23
5.   , 3
6.
  23,  
(
-23
4 
7.  ,  
3 
8. Slope =
[
4/3
3
, y-intercept = -3
5
9. Slope = 3
10. 3x  5 y  26
11. 3x  4 y  13
12. x 
41
23
13. y   5
14. No solution
15. Infinitely many solutions
16. b 
2A
h
17. L 
P  2W
2
18. x 
4y  7
3
19. x  25
20. x  9