CC MATH I STANDARDS UNIT 3
4.5 SOLVING TWO-STEP EQUATIONS: PART 1
WARM UP: Solve part (a) equations, and then use that to find part (b) answers.
4
4
3 1
3a)  11  u  5
1a)  r 
2a) x  
9
9
5 2
1b) What is 3r?
4a)  3s  54
4b) What is 2s?
2b) What is x – 2?
b
5a)  6
7
3b) What is u + 18?
6a)
5b) What is b  14 ?
2
t  14
3
5b) What is
t
?
7
INTRODUCTION TO SOLVING TWO-STEP STEP EQUATIONS:
Find numbers that answer the following questions:
1) What can you double and then add 5 to get 13?
4) What can you double and then add -6 to get -16?
2) What can you triple and then subtract by 7 to
get -1?
5) What can you double and then subtract from 9
to get 5?
3) You can triple and then subtract by 1 to get 29?
6) What can you half and then add 9 to get 15?
SOLVING TWO-STEP EQUATIONS: Verbal explanation by fill in the blanks
#1) 7m – 17 = 60
#3) 7 + 3x = 40
Step One: What minus 17 equals 60?
Step One: 7 plus what equals 40?
– 17 = 60
7+
= 40
Step Two: What times 7 equals previous answer?
Step Two: What times 3 equals previous answer?
7
3
=
#4) 12 + 5y = 27
#2) –2n – 25 = 13
Step One: What minus 25 equals 13?
– 25 = 13
Step Two: What times -2 equals previous answer?
-2
=
Step One: 12 plus what equals 27?
12 +
Step Two: What times 5 equals previous answer?
5
=
= 27
=
TWO-STEP EQUATIONS: Work Backwards
1) Find the VARIABLE.
2) Identify all operations.
3) In REVERSE ORDER of PEMDAS (SADMEP), cancel operations.
4) Use the same number and opposite operations
Operations:
1) 2y – 7 = 23
Operations:
2) 8 + 6x = - 4
Operations:
3) -5r - 18 = 12
Operations:
4) 11 – 7x = 67
PRACTICE: SOLVING TWO-STEP EQUATIONS
1. 7 x  12  2
2. 7a  4  24
3. 4 x  7  37
4. 3 y  9  9
5. 35  8  9 y
6. 8  12 x  32
7. 2 y  3.5  6.5
8. 0  25 x  75
9. 2 x  6  ( 18)
11. 2 g  12  6
12.  28  5 y  8
10.
 9  4m  7
13.  13  7h  1
14. 13d  7  32
15.  41  6 x  5
17. 7 y  2  47
18.  12  5z  37
19. 5n  8  23
20. 25  3  7r
21. 6 x  2  40
22. 3 y  4  14
23. 5 x  ( 9)  26
24. 29  8 y  ( 3)
16.
10  3 x  22
CC MATH I STANDARDS: UNIT 3
4.5 SOLVING TWO-STEP EQUATIONS: PART 2
WARM UP: Solve for the given variable.
1) 3z  5  19
2) 20  7 y  6
3)  9  4 x  21
4)  11  3m  16
5) 15  2 x  7
6)  32  10  6r



SOLVING 2-STEP EQUATIONS WITH FRACTIONS
Solve in reverse order of operations = SADMEP
FRACTIONS represent DIVISION statements.
Be careful for hidden parentheses when there are OPERATIONS in numerator
Option #1:
NO OPERATIONS IN NUMERATOR
n
5  4
3
Option #2:
OPERATIONS IN NUMERATOR
n5
4
3
PRACTICE PROBLEMS
b
 9  2
1)
3
r  15
 6
2)
9
t
 6  10
3)
4
9 p
7
2
t  15
5
5
z
4  6
5)
10
6)
y
7)  4  8
5
m7
3
8)
5
9) 5 
4)
10)
y4
 6
3
11)

13)
3b  12
3
2
14)
27  5a
6
2
x
35
4
1
x  9
2
12)
12  n
 1
7
15)
2s  3
5
7
WORD PROBLEMS INVOLVING MULTI-STEP EQUATIONS:
Write an equation for the problem below and then solve the equation.
1) The product of negative 4 and y increased 2) Eight more than five times a number is
negative 62.
by 11 is equivalent to -5.
3) 8 less than twice a number is twelve.
4) The product of 5 and x decreased by 7 is
as much as 42.
5) How old am I if 400 reduced by 2 times
my age is 244?
6) For a field trip 4 students rode in cars and
the rest filled nine buses. How many
students were in each bus if 472 students
were on the trip?
7) Sarah won 40 super bouncy balls playing 8) You bought a magazine for $5 and four
horseshoes at her school's game night.
erasers. You spent a total of $25. How
Later, she gave two to each of her friends.
much did each eraser cost?
She only has 8 remaining. How many
friends does she have?
9) Two-thirds of a number minus six is –10
10) One-fourth of a number increased by 5 is
as much as 3.
11) 3 fifths of a number less than 9 equals 2
12) 11 minus one-half of a number is -13.