solve the following equation by clearing fractions show all work
want to know if this right
-7/3-5/2x=8+2x
6(-2/3)-(5/2x)(6)=6(8)+2x(6)
14x-15=48+12x
14x-12x-15=48+14x-14x
2x-15=48
2x-15+15=48+14x-14x
2x-15=48
2x-15+15=48+15
2x=-33
2x/2x=-33/2
x=-33/2
How did the -7/3 get change to -2/3? X term is also shifted.
To solve the equation -7/3 - 5/2x = 8 + 2x by clearing fractions, follow these steps:
1. Multiply every term in the equation by the least common multiple (LCM) of the denominators of the fractions, which in this case is 6.
- So, we have: 6(-7/3) - 6(5/2x) = 6(8) + 6(2x)
2. Simplify each term after distribution:
- -14/3 - 30/2x = 48 + 12x
3. Multiply every term by the reciprocal of the coefficient of the variable x to eliminate the fraction:
- 6(-14/3 - 30/2x) = 6(48 + 12x)
- -28/3 - 90/2x = 48 + 12x
4. Combine like terms on both sides of the equation:
- (-90/2x) - 12x = 48 + 28/3
5. Convert mixed numbers to improper fractions:
- (-90/2x) - 12x = 48 + (84/3)
6. Simplify the equation further:
- -90/2x - 12x = 48 + 28/3
- -45/x - 12x = 144/3 + 28/3
- -45/x - 12x = 172/3
7. To get rid of the fractions, multiply every term by 3x:
- (3x)(-45/x - 12x) = (3x)(172/3)
8. Simplify and distribute:
- (-45)(3) - (12)(3x^2) = (3x)(172)
- -135 - 36x^2 = 516x
9. Rearrange the terms to form a quadratic equation:
- 36x^2 + 516x - 135 = 0
10. To solve the quadratic equation, you can use factoring, completing the square, or the quadratic formula.