Solve 4/3(3x-2)-3/5(4x-3)=11/60+3x

$$\frac { 4 } { 3 } ( 3 x - 2 ) - \frac { 3 } { 5 } ( 4 x - 3 ) = \frac { 11 } { 60 } + 3 x$$

Solve for x

$$x=-\frac{3}{4}=-0.75$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{4}{3} by 3x-2.

$$\frac{4}{3}\times 3x+\frac{4}{3}\left(-2\right)-\frac{3}{5}\left(4x-3\right)=\frac{11}{60}+3x$$

Cancel out 3 and 3.

$$4x+\frac{4}{3}\left(-2\right)-\frac{3}{5}\left(4x-3\right)=\frac{11}{60}+3x$$

Express \frac{4}{3}\left(-2\right) as a single fraction.

$$4x+\frac{4\left(-2\right)}{3}-\frac{3}{5}\left(4x-3\right)=\frac{11}{60}+3x$$

Multiply 4 and -2 to get -8.

$$4x+\frac{-8}{3}-\frac{3}{5}\left(4x-3\right)=\frac{11}{60}+3x$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$4x-\frac{8}{3}-\frac{3}{5}\left(4x-3\right)=\frac{11}{60}+3x$$

Use the distributive property to multiply -\frac{3}{5} by 4x-3.

$$4x-\frac{8}{3}-\frac{3}{5}\times 4x-\frac{3}{5}\left(-3\right)=\frac{11}{60}+3x$$

Express -\frac{3}{5}\times 4 as a single fraction.

$$4x-\frac{8}{3}+\frac{-3\times 4}{5}x-\frac{3}{5}\left(-3\right)=\frac{11}{60}+3x$$

Multiply -3 and 4 to get -12.

$$4x-\frac{8}{3}+\frac{-12}{5}x-\frac{3}{5}\left(-3\right)=\frac{11}{60}+3x$$

Fraction \frac{-12}{5} can be rewritten as -\frac{12}{5} by extracting the negative sign.

$$4x-\frac{8}{3}-\frac{12}{5}x-\frac{3}{5}\left(-3\right)=\frac{11}{60}+3x$$

Express -\frac{3}{5}\left(-3\right) as a single fraction.

$$4x-\frac{8}{3}-\frac{12}{5}x+\frac{-3\left(-3\right)}{5}=\frac{11}{60}+3x$$

Multiply -3 and -3 to get 9.

$$4x-\frac{8}{3}-\frac{12}{5}x+\frac{9}{5}=\frac{11}{60}+3x$$

Combine 4x and -\frac{12}{5}x to get \frac{8}{5}x.

$$\frac{8}{5}x-\frac{8}{3}+\frac{9}{5}=\frac{11}{60}+3x$$

Least common multiple of 3 and 5 is 15. Convert -\frac{8}{3} and \frac{9}{5} to fractions with denominator 15.

$$\frac{8}{5}x-\frac{40}{15}+\frac{27}{15}=\frac{11}{60}+3x$$

Since -\frac{40}{15} and \frac{27}{15} have the same denominator, add them by adding their numerators.

$$\frac{8}{5}x+\frac{-40+27}{15}=\frac{11}{60}+3x$$

Add -40 and 27 to get -13.

$$\frac{8}{5}x-\frac{13}{15}=\frac{11}{60}+3x$$

Subtract 3x from both sides.

$$\frac{8}{5}x-\frac{13}{15}-3x=\frac{11}{60}$$

Combine \frac{8}{5}x and -3x to get -\frac{7}{5}x.

$$-\frac{7}{5}x-\frac{13}{15}=\frac{11}{60}$$

Add \frac{13}{15} to both sides.

$$-\frac{7}{5}x=\frac{11}{60}+\frac{13}{15}$$

Least common multiple of 60 and 15 is 60. Convert \frac{11}{60} and \frac{13}{15} to fractions with denominator 60.

$$-\frac{7}{5}x=\frac{11}{60}+\frac{52}{60}$$

Since \frac{11}{60} and \frac{52}{60} have the same denominator, add them by adding their numerators.

$$-\frac{7}{5}x=\frac{11+52}{60}$$

Add 11 and 52 to get 63.

$$-\frac{7}{5}x=\frac{63}{60}$$

Reduce the fraction \frac{63}{60} to lowest terms by extracting and canceling out 3.

$$-\frac{7}{5}x=\frac{21}{20}$$

Multiply both sides by -\frac{5}{7}, the reciprocal of -\frac{7}{5}.

$$x=\frac{21}{20}\left(-\frac{5}{7}\right)$$

Multiply \frac{21}{20} times -\frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{21\left(-5\right)}{20\times 7}$$

Do the multiplications in the fraction \frac{21\left(-5\right)}{20\times 7}.

$$x=\frac{-105}{140}$$

Reduce the fraction \frac{-105}{140} to lowest terms by extracting and canceling out 35.

$$x=-\frac{3}{4}$$