Math 10031 Chapter 2, Sec. 2 Introduction to Solving Equations
Supplemental Problems
Determine which of the following are expression and which are equations.
1. 4x  3x 10
3.
4
x3
5
2.
4.
4x  3x  10  5x  3
4
1
x  3  7x 
5
2
Determine if the given value is the solution to the equation. Give your explanations.
5. 2m  3  7 ; 5
7.
y
1 5 3
 ;
3 12 4
6. x  3  9 ; 6
8.
3m 24

;
2
5
16
5
Solve the following linear equations, it maybe helpful to simplified first before solving for the
unknown variable.
9. 5x 14x 10  12  6x  4
10. 5m  7m
11.
4a  10a  28
12.
29  2x  5  3x  6  5x 15x
13.
2  (4 y  5)  3 y  4
14.
4( x  3)  2(5 x  4)
15.
2
y  18
3
16.

m 7

5 20
17.
2
x  9  11
5
18.
2t  (1  4t )  10t
19.
3(2a  1)  5  4a  3  3(3a  7)
20.
4.7 y  7.2  1.2 y  62.8
Math 10031 Chapter 2, Sec. 2 Introduction to Solving Equations
Supplemental Problems
21. 2t  5.56  6t  2.44
22.
4v
7
 5v 
5
25
23. 5x  2 3x  4( x  3)  2 x  6
24.
3n  7
5
10
In exercises 25 – 28, solve for the unknown variable. If no equation is given, perform the
indicated operations to simplify the algebraic expressions.
25. 5(12  r )  15
26. 5(12  x)  15  3x
27.
7  14(4  x)  9  6 x
28.
7  14(4  x)  32  6 x
In exercises 29 – 32, find the solution to each equation. Some may have more than one
solution, some may have no solution. ( These are the special case equations)
29. 3(2  x)  (3 x  4)  10
30.
5  3(3x  6)  1  3x  14  6 x
31.
9 x  (7 x  2)4  3x  2(4  14 x)  6 x
32.
9 x  (7 x  2)4  3x  2(5  14 x)  6 x
Math 10031 Chapter 2, Sec. 2 Introduction to Solving Equations
Supplemental Problems
Answers to Supplemental Problems to Chapter 2, Sec. 2
1. Expression
21. t  2
2. Equation
22. v  
3. Expression
23. x  6
4. Equation
24.
5. Yes
25. Equation; r  15
6. No
26. Expression; 75  8x
7. Yes
27.
8. Yes
28. Expression; 54  20x
9. x 
2
3
7
105
n  19
Equation; x 
29. All reals
10. m  0
30. No Solution
11. a  2
31. All reals
12. x  2
32. No Solution
13. y  1
14. x 
15.
10
3
y  27
16. m  
7
4
17. x  50
18. t  
1
4
19. a  10
27
4
Math 10031 Chapter 2, Sec. 2 Introduction to Solving Equations
Supplemental Problems
20.
y  20