6th Grade Math Textbook, Fundamentals

Solve: 21  c 5

21  5  c 5  5 Subtract 5 from both sides.

16  c Simplify.

()^16 ()()c Multiply by the reciprocal of.

64 c

1

4

4

1

4

1

1

4

1

4

1

4

1

4

1

 &KDSWHU

5-16

Update your skills. See page 415 XVIII.

Solve Two-Step Equations

with Fractions

Objective To solve two-step algebraic equations with fractions

and mixed numbers by applying the appropriate properties of equality

and the Inverse Properties of Addition and Multiplication

Sean spends hour playing songs he knows. Then he

spends hour practicing each new song he is learning.

If Sean spends 2 hours practicing today, how many

new songs is he learning?

To find the number of new songs Sean is learning,

write and solve a two-step equation.

Let sthe number of new songs Sean is learning.

(^12)  (^34) s (^234)
3
4
3
4
1
2
number of new songs
total number of hours spent practicing
hours spent on
old songs
hours spent on
each new song
Solve:  s 2
  s 2 
s 2 Simplify.
()s()^2
s • Rename the mixed number.
s Simplify, then multiply.
s 3
So Sean is learning 3 new songs.
Use the Subtraction Property
of Equality to “undo” addition.
4
3
9
4
1
1
3
1
9
4
4
3
1
4
4
3
3
4
4
3
1
4
3
4
1
2
3
4
3
4
1
2
1
2
3
4
3
4
1
2
Multiply both sides by , the
reciprocal of , to isolate^34 s.
4
3
Check:  s 2
 (3) 2 Substitute 3 for s.
 2 Multiply.
 2
2  2 Tr u e
9
4
1
2
3
4
(^2) ?
4
3
4
3
4
3
4
(^9) ?
4
3
4
(^3) ?
4
1
2
3
4
3
4
1
2
Check: 21  c 5
21 (64)  5 Substitute 64 for c.
21 16  5
21  21 Tr u e
1
4
1
4
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