Solving an Equation with Fractions as CoefficientsSolve
Step 1 The LCD of all the fractions in the equation is 6.
Multiply.
Combine like terms.Step 2 Add x.
Combine like terms.Step 3 Divide by 2.
Step 4 CHECK Original equation
LetMultiply.✓ True
The solution, - 6 , checks, so the solution set is 5 - 66. NOW TRY
- 1 =- 1
- 4 + 3 1 - 2
x=- 6.
2
3
1 - 62 -
1
2
1 - 62 -
1
6
1 - 62 - 2
2
3
x-
1
2
x=-
1
6
x- 2
x=- 6
2 x
2
=
- 12
2
2 x=- 12
x+x=-x- 12 + x
x=-x- 12
4 x- 3 x=-x- 12
6 a
2
3
xb + 6 a-
1
2
xb = 6 a-
1
6
xb + 61 - 22
6 a
2
3
x-
1
2
xb = 6 a-
1
6
x- 2 b
2
3
x-
1
2
x=-
1
6
x- 2
23 x-
12 x=-^
16 x-2.
EXAMPLE 6
SECTION 2.3 More on Solving Linear Equations 101
CAUTION When clearing an equation of fractions, be sure to multiply every
term on each side of the equation by the LCD.
NOW TRY
EXERCISE 6
Solve.
1
2x+5
8
x=3
4
x- 6Multiply each side by
6, the LCD.
Distributive property;
multiply eachterm
inside the parentheses
by 6.Solving an Equation with Fractions as CoefficientsSolve.
Step 1
Distributive propertyMultiply.
Distributive property- 4 x+ 7 = 15 Combine like terms.
5 x+ 25 - 9 x- 18 = 15
5 1 x+ 52 - 9 1 x+ 22 = 15
15 B
1
3
1 x+ 52 R + 15 B-
3
5
1 x+ 22 R= 15112
15 B
1
3
1 x+ 52 -
3
5
1 x+ 22 R= 15112
1
3
1 x+ 52 -
3
5
1 x+ 22 = 1
13 1 x+^52 -
35 1 x+^22 =^1
EXAMPLE 7
The fractions have
been cleared.Clear the fractions.
Multiply by 15, the LCD.NOW TRY ANSWER
- 5 - 166
Pay particular
attention here.= 51 x+ 52= 15 # 13 # 1 x+ 52
15 C^13 1 x+ 52 D