Download document

Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
(For help, go to Lesson 2-3.)
Simplify each expression.
1. 2x + 4 + 3x
2. 5y + y
4. 2 – 4c + 5c
5. 4x + 3 – 2(5 + x)
3. 8a – 5a
Check Skills You’ll Need
7-2
Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
Solutions
1. 2x + 4 + 3x = (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
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 = 41
Combine like terms.
4s + 5 – 5 = 41 – 5 Subtract 5 from each side.
4s = 36
Simplify.
4s
36
=
4
4
Divide each side by 4.
s=9
Simplify.
7-2
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 9 + 32 = 41, the solution is reasonable.
Quick Check
7-2
Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
The sum of three consecutive integers is 42. Find
the integers.
Words
sum of three consecutive integers
Let
is
42
=
42
n = the least integer.
Then n + 1 = the second integer,
and n + 2
Equation
= the third integer.
n + n+1 + n+2
7-2
Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
(continued)
n + (n + 1) + (n + 2) = 42
(n + n + n) + (1 + 2) = 42
3n + 3 = 42
Use the Commutative and
Associative Properties of Addition to
group like terms together.
Combine like terms.
3n + 3 – 3 = 42 – 3 Subtract 3 from each side.
3n = 39
Simplify.
3n
39
=
3
3
Divide each side by 3.
n = 13
Simplify.
7-2
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
13 + 14 + 15 = 42.
Quick Check
7-2
Solving Multi-Step Equations
PRE-ALGEBRA LESSON 7-2
Solve each equation.
a. 4(2q – 7) = –4
4(2q – 7) = –4
8q – 28 = –4
8q – 28 + 28 = –4 + 28
Use the Distributive Property.
Add 28 to each side.
8q = 24
Simplify.
8q
24
=
8
8
Divide each side by 8.
q=3
Simplify.
7-2
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.
24 –6r
= –6
–6
Divide each side by –6.
–4 = r
Simplify.
7-2
Quick Check