[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \frac{1}{5} (4 - 3x) = \frac{1}{7} (3x - 4) \\ [/tex]
Use the distributive property to multiply 1/5 by 4-3x.
[tex]\frac{1}{5}\times 4+\frac{1}{5}\left(-3\right)x=\frac{1}{7}\left(3x-4\right) \\ [/tex]
Multiply 1/5 and 4 to get 4/5.
[tex]\frac{4}{5}+\frac{1}{5}\left(-3\right)x=\frac{1}{7}\left(3x-4\right) \\ [/tex]
Multiply 1/5 and -3 to get -3/5.
[tex]\frac{4}{5}+\frac{-3}{5}x=\frac{1}{7}\left(3x-4\right) \\ [/tex]
Use the distributive property to multiply 1/7 by 3x-4.
[tex]\frac{4}{5}-\frac{3}{5}x=\frac{1}{7}\times 3x+\frac{1}{7}\left(-4\right) \\ [/tex]
Multiply 1/7 and 3 to get 3/7 & 1/7 × -4 to get -4/7.
[tex]\frac{4}{5}-\frac{3}{5}x=\frac{3}{7}x-\frac{4}{7} \\ [/tex]
Subtract [tex]\frac{3}{7}x\\[/tex] from both sides.
[tex]\frac{4}{5}-\frac{3}{5}x-\frac{3}{7}x=-\frac{4}{7} \\ [/tex]
Combine [tex]-\frac{3}{5}x\\[/tex] and [tex]-\frac{3}{7}x\\[/tex] to get [tex]-\frac{36}{35}x\\[/tex].
[tex]\frac{4}{5}-\frac{36}{35}x=-\frac{4}{7} \\ [/tex]
Subtract 4/5 from both sides.
[tex]-\frac{36}{35}x=-\frac{4}{7}-\frac{4}{5} \\ [/tex]
The least common multiple of 7 and 5 is 35. Convert -4/7 and 4/5 to fractions with denominator 35.
[tex]-\frac{36}{35}x=-\frac{20}{35}-\frac{28}{35} \\ [/tex]
Because [tex]-\frac{20}{35} \\[/tex] and [tex]\frac{28}{35}\\[/tex] have the same denominator, subtract them by subtracting their numerators.
[tex]-\frac{36}{35}x=\frac{-20-28}{35} \\ [/tex]
Subtract 28 from -20 to get -48.
[tex]-\frac{36}{35}x=-\frac{48}{35} \\ [/tex]
Multiply both sides by [tex]-\frac{35}{36}\\[/tex], the reciprocal of [tex]-\frac{36}{35}\\[/tex].
[tex]x=-\frac{48}{35}\left(-\frac{35}{36}\right) \\ [/tex]
Multiply [tex]-\frac{48}{35}\\[/tex] by [tex]-\frac{35}{36}\\[/tex] by multiplying the numerator by the numerator and the denominator by the denominator.
[tex]x=\frac{-48\left(-35\right)}{35\times 36} \\ [/tex]
Carry out the multiplications in the fraction [tex]\frac{-48\left(-35\right)}{35\times 36}\\[/tex].
[tex]x=\frac{1680}{1260} \\ [/tex]
Reduce the fraction 1680/1260 to its lowest terms by extracting and cancelling out 420.
[tex] \huge \boxed{ \boxed{ \bf \: x=\frac{4}{3} \approx \: 1.33}}[/tex]
