Page 678 - Algebra 1

b. _x=_3
4 x-1
SOLUTION
_x = _3
4 x-1
x(x - 1) = 12 x2-x=12
x2 -x-12=0 (x - 4)(x + 3) = 0
Use cross products.
Distribute x over (x - 1).
Subtract 12 from both sides.
Factor.
Use the Zero Product Property to solve.
x = 4 or x = -3
Check Verifythatthesolutionisnotextraneous.
_x = _3 ; x = 4 or _x = _3 ; x = -3
3 _-3 Substitute.
44
The solution set is {4, -3}.
If a rational equation includes a sum or difference, find the LCD of all the
terms to solve.
Using the LCD to Solve Addition Equations
x 2x SOLUTION
__
3 + 16 = 11
Multiply each term by the LCD.
Simplify each term. Add.
Divide both sides by 22.
4
_4 4
x-1 3
_x-1 4_
4 - 1 4 -3 - 1 1 = 1 ✓ Simplify each fraction. -_3 = -_3 ✓
Example
2
__
Solve 3 + 16 =11.
Hint
To find the LCD of the terms, consider the denominator of the whole number to be 1.
x 2x
The LCD of the denominators is 2x.
__
(2x) 3 + (2x) 16 = (2x)11
x 2x
6 + 16 = 22x
22 = 22x 1 = x
Check Verifythatthesolutionisnotextraneous. __
Substitute 1 for x in the original equation. Simplify.
3 + 16 = 11 x 2x
__
3 + 16 11
1 2(1)
11 = 11 ✓
The solution is x = 1.
Lesson 99 663