# 1: solving equations involving fractions

```MAT 0024
SOLVING EQUATIONS INVOLVING FRACTIONS
Worksheet 3
Sections 2.1 &amp; 2.2
Summary: To solve equations, use the addition/multiplication principles to “Get rid of…”
1. Parentheses by using the distributive property. If no fractions, combine like terms.
2. Denominators: Multiply each side of equation by common denominator.
Decimals: Multiply each side of equation by 10, 100, 1000, etc. COMBINE LIKE TERMS.
BEFORE NEXT STEP EACH SIDE SHOULD BE NO MORE COMPLICATED THAN:
“4x – 8”
Get variable terms on one side of the equation and all constant terms on the
other side. Goal: Each side of equation is no more complicated than
“4x = -9.”
4. Coefficients by dividing by coefficient (BY SAME NUMBER). Goal: x = number
Parents, Do Send Cash
1.
m
 3
4
2.
5.
2
x6
7
6.  5 
9.
3
2
t
4
3
10.
13. 2 y 
3 1

5 2
1
x5
4
x
6
2
3
 t
3
5
14. y 
3.
t
6
3
4.  6 
7.
m
 5
8
8.
11.
5
3
x
6
4
2
1

5
3
3x
5
m
2
3
12.
3
1
x
4
2
15.
1 1
 t4
4 2
16.
1
1
x  x  3  x
4
2
19.
2
 x  2  3
5
22.
1 2
1
 t 1  t  t
2 5
5
25. 3.5X + 0.8 = 18.24 - 5.9X
17.
20.
1
3
 2m  m 
3
2
3
2 x  1  2
4
23.
18. m 
21.
1
2
2
m 2  m
5
3
5
24. 
2 1
 m 1
3 4
2
3x  1  5
3
1
1
w3 w
4
3
26. 0.3X - .24 = 0.36 + .52X
PAGE 75: Odds 47 – 57, 61, 63
P. 83: 29, 30, all 45 – 52, 73, 75, 77
2
[even answers: P. 83: 30)8; 46)  ;48)-3;50)-3, 52) 0.8]
3
(024)
```