Download Algebra 1 2.1 Solving One-Step and Two

Algebra 1
2.1 Solving One-Step and Two-Step Equations
NOTES:
1.
Expression vs Equation
Expression:
Equation:
2.
Simplify vs Solve
Simplify:
Solve:
3.
Like terms:
4.
Solution:
5.
Checking a solution:
6.
Inverse Property
Of Addition:
Of Multiplication:
Examples:
Simplify each expression.
1.
3 + 4x – 5 + 7x
2.
-x – 5 – 8 + 6x
Solve each equation using the inverse property. Check your solution.
1. x + 22 = 48
2.
y – 15 = -16
3.
-13 + g = -5
4. 5z = 45
5.
15 = -6a
6.
-b = -5
8.
x
 2
3
9.
10. 2y + 8 = 12
11.
-3a – 2 = 16
12.
6m - 5 = -7
13. –p – 10 = 1
14.
x
 8  12
4
15.
18 
7.
3
x 2
4
14 
x
7
2
x  15
3
2.1 ASSIGNMENT:
NAME: __________________
Describe the difference in the process for solving the two given equations.
1. a. x + 7 = 18
b. x – 7 = 18
2.
Difference:
a. -3x = 9
b. -3 + x = 9
Difference:
Solve each equation below by using the inverse operation. Show your work.
3. a – 16 = 15
4. m + 54 = 36
5. 11 = t + 29
y
3
6. 7x = 56
7.
9. 6 + y = 12
10. x - 59 = -42
11. -4 + m = -3
13. -7x = -14
14.
12.
b
 6
9
 13 
Reference Glencoe Textbook: Pages83-95 Chapters 2-2 and 2-3
8. -15f = 3
b
 1
15
In Problems 15-16, write, in words, the first and second steps necessary to solve
each equation. Do not solve.
15. 4x – 10 = 14
16. -15 – 2x = -13
First Step:
First Step:
Second Step:
Second Step:
Solve each equation below. Show all work.
x
17. -4x – 7 = 25
 5  15
18.
4
20. 15  7 
z
6
21. 11 - 2q = 5
Reference Glencoe Textbook: Pages83-95 Chapters 2-2 and 2-3
19. –p + 10 = -25
22. 9 -
b
 12
5
WRITE and SOLVE an equation for each situation.
23. Jill has saved $137 toward the
24. John is 25 years old. If John is
purchase of a mountain bike. The
twice Andy’s age plus 3 years, How
bike costs $547. WRITE and
old is Andy?
SOLVE an equation to find out how
much more money she needs.
Equation:
Equation:
Andy’s Age:
Solution:
25.
The length of line segment AC
below is 22 units. If the length
of AB is 14 units, WRITE and
SOLVE an equation to find the
length of BC.
26.
The length of line segment AC is
78 units. Segment AB is 4x and
segment BC is 26. What is the
length of AB?
78 units
22 units
C
B
A
14 units
Equation:
Length of BC:
x
C
B
A
4x units
Equation:
Length of AB:
Reference Glencoe Texbook: Pages83-95 Chapters 2-2 and 2-3
26 units
ANSWERS:
1. In a. you subtract 7 from both sides, and in b. you add 7 to both sides.
2. a. divide -3 b. add 3
3. a = 31
4. m = -18
5. t = -18
6. x=8
7. y = -39
8. f = -1/5
9. y=6
10. x = 17
11. m = 1
12. b = -54
13. x=2
14. b = -15
15. Add 10; Divide 4
16. Add 15; Divide -2
17. x=-8
18. x=40
19. p=35
20. z=-132
21. q=3
22. b=-15
23. x + 137 = 547 x = $410
24. 2a+3=25 a = 11
25. 14 + x = 22 BC = 8 units
26. 4x + 26 = 78 AB = 52