1. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
(For help, go to Lesson 2-3.)
Simplify each expression.
1. 2x x 2. 5y + y 3. 8a – 5a
4. 2 – 4c + 5c 5. 4x + 3 – 2(5 + x)
Check Skills You’ll Need
7-2

2. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
Solutions
1. 2x x = (2 + 3)x + 4
= 5x + 4
2. 5y + y = 5y + 1y
= (5 + 1)y
= 6y
3. 8a – 5a = (8 – 5)a
= 3a
4. 2 – 4c + 5c = 2 + (–4c + 5c)
= 2 + (–4 + 5)c
= 2 + c
5. 4x + 3 – 2(5 + x) = 4x + 3 – 10 – 2x
= 4x – 2x – 7
= (4 – 2)x – 7
= 2x – 7
7-2

3. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
In his stamp collection, Jorge has five more than three times as many stamps as Helen. Together they have 41 stamps. Solve the equation s + 3s + 5 = 41. Find the number of stamps each one has.
s + 3s + 5 = 41
4s + 5 = Combine like terms.
4s + 5 – 5 = 41 – 5   Subtract 5 from each side.
4s = Simplify.
= Divide each side by 4. 4s 4 36
s = Simplify.
7-2

4. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
(continued)
Helen has 9 stamps. Jorge has 3(9) + 5 = 32 stamps.
Check   Is the solution reasonable? Helen and Jorge have a total of 41 stamps. Since = 41, the solution is reasonable.
Quick Check
7-2

5. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
The sum of three consecutive integers is 42. Find the integers.
sum of three consecutive integers 42 is
Words
Let = the least integer. n
Then = the second integer,
n + 1
and = the third integer.
n + 2 n
n + 1
n + 2
Equation 42 =
7-2

6. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
(continued)
n + (n + 1) + (n + 2) = 42
(n + n + n) + (1 + 2) = 42 Use the Commutative and Associative Properties of Addition to group like terms together.
3n + 3 = 42 Combine like terms.
3n + 3 – 3 = 42 – 3   Subtract 3 from each side.
3n = 39 Simplify.
n = 13 Simplify.
= Divide each side by 3. 3n 3 39
7-2

7. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
(continued)
If n = 13, then n + 1 = 14, and n + 2 = 15. The three integers are 13, 14, and 15.
Check Is the solution reasonable? Yes, because = 42.
Quick Check
7-2

8. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
Solve each equation.
a. 4(2q – 7) = –4
4(2q – 7) = –4
8q – 28 = –4
Use the Distributive Property.
8q – = –4 + 28
Add 28 to each side.
8q = 24
Simplify.
Divide each side by 8. = 8q 8 24
q = 3
Simplify.
7-2

9. Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
(continued)
b.    44 = –5(r – 4) – r
44 = –5(r – 4) – r
44 = –5r + 20 – r
Use the Distributive Property.
44 = –6r + 20
Combine like terms.
44 – 20 = –6r + 20 – 20
Subtract 20 from each side.
24 = –6r
Simplify.
Divide each side by –6. = 24 –6
–6r
Quick Check
–4 = r
Simplify.
7-2