Question

Which number can each term of the equation be multiplied by to illuminate the fractions before solving 6-3/4x+1/3=1/2x+5

Answer 1

`\boldsymbol{\sf{6-(3)/(4)x+(1)/(3)=(1)/(y)x+5 }}`

Convert 6 to the fraction 18/3.

`\boldsymbol{\sf{(18)/(3) -(3)/(4)x+(1)/(3)=(1)/(y)x+5 }}`

Since the fractions 18/3 and 1/3 have the same denominator, we add their numerators to calculate them.

`\boldsymbol{\sf{(18+1)/(3)-(3)/(4)x=(1)/(2)x+5 \ \longmapsto \ \ [Add \ 18+1] }}`

`\boldsymbol{\sf{(19)/(3)-(3)/(4)x=(1)/(2)x+5 }}`

Subtract
`\bf{(1)/(2)x }` on both sides.

`\boldsymbol{\sf{(19)/(3)-(3)/(4)x-(1)/(2)x=5 }}`

Combine
`\bf{-(3)/(4)x}` and
`\bf{-(1)/(2)x}` to get
`\bf{-(5)/(4)x}`.

`\boldsymbol{\sf{(19)/(3)-(5)/(4)x=5 }}`

Subtract 19x from both sides.

`\boldsymbol{\sf{-(5)/(4)x=5-(19)/(3) }}`

Convert 5 to the fraction 15/3.

`\boldsymbol{\sf{-(4)/(5)x=(15)/(3)-(19)/(3) }}`

Since the fractions 15/3 and 19/3 have the same denominator, we add their numerators to calculate them.

`\boldsymbol{\sf{-(5)/(4)x=(15-19)/(3) \ \longmapsto \ \ [Subtract \ 15-19] }}`

`\boldsymbol{\sf{-(5)/(4)x=-(4)/(3) }}`

Multiply both sides by -4/3, the reciprocal of -4/3.

`\boldsymbol{\sf{x=-(4)/(5)\left(-(4)/(5)\right) }}`

Multiply -4/3 by -4/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

`\boldsymbol{\sf{x=(-4(-4))/(3*5) \ \ \longmapsto \ \ Multiply, \ numerator \ and \ denominator. }}`

`\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ \ \ x=(16)/(15) }}}}}`