Question

1/5 (4-3x) = 1/7 (3x - 4)

pls solve it pls pls

Answer 1

`\huge \boxed{\mathfrak{Question} \downarrow}`

• 
  `\large\sf(1)/(5) (4 - 3x) = (1)/(7) (3x - 4) \\`

`\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}`

`(1)/(5) (4 - 3x) = (1)/(7) (3x - 4) \\`

Use the distributive property to multiply 1/5 by 4-3x.

`(1)/(5)* 4+(1)/(5)\left(-3\right)x=(1)/(7)\left(3x-4\right) \\`

Multiply 1/5 and 4 to get 4/5.

`(4)/(5)+(1)/(5)\left(-3\right)x=(1)/(7)\left(3x-4\right) \\`

Multiply 1/5 and -3 to get -3/5.

`(4)/(5)+(-3)/(5)x=(1)/(7)\left(3x-4\right) \\`

Use the distributive property to multiply 1/7 by 3x-4.

`(4)/(5)-(3)/(5)x=(1)/(7)* 3x+(1)/(7)\left(-4\right) \\`

Multiply 1/7 and 3 to get 3/7 & 1/7 × -4 to get -4/7.

`(4)/(5)-(3)/(5)x=(3)/(7)x-(4)/(7) \\`

Subtract
`(3)/(7)x\\` from both sides.

`(4)/(5)-(3)/(5)x-(3)/(7)x=-(4)/(7) \\`

Combine
`-(3)/(5)x\\` and
`-(3)/(7)x\\` to get
`-(36)/(35)x\\`.

`(4)/(5)-(36)/(35)x=-(4)/(7) \\`

Subtract 4/5 from both sides.

`-(36)/(35)x=-(4)/(7)-(4)/(5) \\`

The least common multiple of 7 and 5 is 35. Convert -4/7 and 4/5 to fractions with denominator 35.

`-(36)/(35)x=-(20)/(35)-(28)/(35) \\`

Because
`-(20)/(35) \\` and
`(28)/(35)\\` have the same denominator, subtract them by subtracting their numerators.

`-(36)/(35)x=(-20-28)/(35) \\`

Subtract 28 from -20 to get -48.

`-(36)/(35)x=-(48)/(35) \\`

Multiply both sides by
`-(35)/(36)\\`, the reciprocal of
`-(36)/(35)\\`.

`x=-(48)/(35)\left(-(35)/(36)\right) \\`

Multiply
`-(48)/(35)\\` by
`-(35)/(36)\\` by multiplying the numerator by the numerator and the denominator by the denominator.

`x=(-48\left(-35\right))/(35* 36) \\`

Carry out the multiplications in the fraction
`(-48\left(-35\right))/(35* 36)\\`.

`x=(1680)/(1260) \\`

Reduce the fraction 1680/1260 to its lowest terms by extracting and cancelling out 420.

`\huge \boxed{ \boxed{ \bf \: x=(4)/(3) \approx \: 1.33}}`