Question

solve: 2/3(x) -1/4 = x/6 + 3/2

Answer 1

@phi @texaschic101 @DanielJ

Answer 2

is it
\[ \frac{2}{3} x - \frac{1}{4} = \frac{x}{6} + \frac{3}{2} \]

Answer 3

yep

Answer 4

why don't you multiply everything y the common denominator to get rid of the fractions

Answer 5

typo....multiply everything by common denominator

Answer 6

\[\frac{ 2 }{ 3x } - \frac{ 1 }{ 4 } = \frac{ x }{ 6 } + \frac{ 3 }{ 2 }\]
Take all of your x's to one side, and be careful of your signs
\[\frac{ 2 }{ 3x } - \frac{ x }{ 6 } = \frac{ 3 }{ 2 } + \frac{ 1 }{ 4 }\]
Simplify each side as far as possible
\[\frac{ 2(6) - x(3x) }{ (3x)(6) } = \frac{ 7 }{ 4 }\]
\[\frac{ 12 - 3x^{2} }{ 18x } = \frac{ 7 }{ 4 }\]
\[\frac{ 3(4 -x ^{2}) }{ 18x } = \frac{ 7 }{ 4 }\]
\[\frac{ 4- x ^{2} }{ 6x } = \frac{ 7 }{ 4 }\]
Next, find the lowest common denominator
\[\frac{ 4(4 - x ^{2}) }{ 6x(4) } = \frac{ 7(6x) }{ 6x(4) }\]
Multiply each side by 6x(4)
\[4(4 - x ^{2}) = 7(6x)\]
Simplify to try to get 0 on the right hand side
\[4(4 - x ^{2}) -7(6x) = 0\]
Expand the brackets
\[16 - 4x ^{2} -42x = 0\]
Re-arrange and divide both sides by a common factor (-2)
\[2x ^{2} + 21x -8 = 0\]
This cannot be factorised so we use the quadratic formula
\[x = \frac{ -b \pm \sqrt{b ^{2} - 4ac} }{ 2a }\]
\[x = \frac{ -21 \pm \sqrt{21 ^{2} - 4(2)(-8)} }{ 2(2) }\]
\[x = \frac{ -21 \pm \sqrt{441 - 4(-16)} }{ 4 }\]
\[x = \frac{ -21 \pm \sqrt{441 + 64} }{ 4 }\]
\[x = \frac{ -21 \pm \sqrt{505} }{ 4 }\]
And then solve:
\[x = 0.3680512636\]
or
\[x = -10, 86805126\]

Answer 7

Wait, my method is wrong. It's \[\frac{ 2 }{ 3 }x - \frac{ 1 }{ 4 } = \frac{ x }{ 6 } + \frac{ 3 }{ 2 }\] not \[\frac{ 2 }{ 3x } - \frac{ 1 }{ 4 } = \frac{ x }{ 6 } + \frac{ 3 }{ 2 }\]

Should i redo it?

Answer 8

(2/3) x - 1/4 = x/6 + 3/2 --- multiply by 12
8x - 3 = 2x + 18
8x - 2x = 18 + 3
6x = 21
x = 21/6
x = 7/2

check..
(2/3)(7/2) - 1/4 = (7/2) / 6 + 3/2
7/3 - 1/4 = (7/2 * 1/6) + 3/2
28/12 - 3/12 = 7/12 + 18/12
25/12 = 25/12 (correct)

x = 7/2

Answer 9

@texaschic101 Yeap, that's correct! I can't believe i made such a stupid mistake...

Answer 10

If I had $1 for every mistake I made, I would be rich

Answer 11

Let's get rich together then! :P @Dara08 does this solve your problem?

Answer 12

:)

Answer 13

@Dara08 ...if you have any questions, please ask

Answer 14

Thankyou so much guys! its really a big help thanks thanks

Answer 15

@texaschic101 can you explain how it became 8x - 3 = 2x + 18 multiplied by 12

Answer 16

12 is the lowest common denominator of all of the values, so it becomes
\[\frac{ 2 }{ 3 } x \times 12 - \frac{ 1 }{ 4 } \times 12 = \frac{ x }{ 6 } \times 12 + \frac{ 3 }{ 2 } \times 12\] which is \[\frac{ 24 }{ 3 } x - \frac{ 12 }{ 4 } = \frac{ 12x }{ 6 } + \frac{ 36 }{ 2 }\] which can be simplified to \[8x - 3 = 2x + 18\]

Answer 17

thankyou :)

Answer 18

@Dara08 Let us know if you have any more problems!

Answer 19

@DanielJ can u explain the X^2+x -6x-6=0 that one im so sorry for bothering hehh

Answer 20

\[x ^{2} - 5x -6 =0\]
Isn't factorisable as is, so you add x and minus x to make is factorisable using common factors\[x ^{2} + x - 6x -6 = 0\]and then group and take out common factors\[x(x + 1) -6(x + 1) = 0\]\[(x - 6)(x + 1) = 0\]Because it equals 0, either x - 6 = 0 or x + 1 = 0

Which means x = 6 or x = -1

Answer 21

i see. thankyou again!

Answer 22

You're welcome! I'm always happy to help!