Question

solve the equation 2/3 (3x-2) = 4/5 (2x-3) - 4/3​

Answer 1

Solution :-

$\purple{{\bf\leadsto \dfrac{2}{3} (3x - 2) = \dfrac{4}{5} (2x - 3) - \dfrac{4}{3}}}$

Multiply the fraction outside the bracket with numbers in bracket.

${\tt\leadsto \dfrac{6}{3}x - \dfrac{4}{3} = \dfrac{8}{5}x - \dfrac{12}{15} - \dfrac{4}{3}}$

Write all the numerators with one common denominator by converting them into like fractions.

${\tt \leadsto \dfrac{6x - 4}{3} = \dfrac{24x - 12 - 20}{15}}$

Shift the denominator on LHS to RHS.

${\tt \leadsto 6x - 4 = \cancel{3} \bigg( \dfrac{24x - 12 - 20}{\cancel{15}} \bigg)}$

Write the obtaining fraction.

${\tt\leadsto 6x - 4 = \dfrac{24x - 12 - 20}{5}}$

Shift the number 5 from RHS to LHS.

${\tt \leadsto 5(6x - 4) = 24x - 12 - 20}$

Multiply the number 5 with the numbers in bracket.

${\tt\leadsto 30x - 20 = 24x - 12 - 20}$

Subtract the constants on RHS.

${\tt\leadsto 30x - 20 = 24x - 32}$

Shift the variable on RHS to LHS and the constant on LHS to RHS.

${\tt \leadsto 30x - 24x = ( - 32) + 20}$

Subtract the values on LHS and add the values on RHS.

${\tt\leadsto 6x = ( - 12)}$

Shift the number 6 from LHS to RHS.

${\tt \leadsto x = \dfrac{( - 12)}{6}}$

Simplify the fraction to get the value of x.

$\purple{{\bf\leadsto x = ( - 2)}}$

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