Solve 7/5(3x-8)+1/3(5x-2)=1/4(x+4)+2/3(x-3)

$$\frac { 7 } { 5 } ( 3 x - 8 ) + \frac { 1 } { 3 } ( 5 x - 2 ) = \frac { 1 } { 4 } ( x + 4 ) + \frac { 2 } { 3 } ( x - 3 )$$

Solve for x

$$x = \frac{652}{297} = 2\frac{58}{297} \approx 2.195286195$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{7}{5} by 3x-8.

$$\frac{7}{5}\times 3x+\frac{7}{5}\left(-8\right)+\frac{1}{3}\left(5x-2\right)=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Express \frac{7}{5}\times 3 as a single fraction.

$$\frac{7\times 3}{5}x+\frac{7}{5}\left(-8\right)+\frac{1}{3}\left(5x-2\right)=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Multiply 7 and 3 to get 21.

$$\frac{21}{5}x+\frac{7}{5}\left(-8\right)+\frac{1}{3}\left(5x-2\right)=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Express \frac{7}{5}\left(-8\right) as a single fraction.

$$\frac{21}{5}x+\frac{7\left(-8\right)}{5}+\frac{1}{3}\left(5x-2\right)=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Multiply 7 and -8 to get -56.

$$\frac{21}{5}x+\frac{-56}{5}+\frac{1}{3}\left(5x-2\right)=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Fraction \frac{-56}{5} can be rewritten as -\frac{56}{5} by extracting the negative sign.

$$\frac{21}{5}x-\frac{56}{5}+\frac{1}{3}\left(5x-2\right)=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Use the distributive property to multiply \frac{1}{3} by 5x-2.

$$\frac{21}{5}x-\frac{56}{5}+\frac{1}{3}\times 5x+\frac{1}{3}\left(-2\right)=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Multiply \frac{1}{3} and 5 to get \frac{5}{3}.

$$\frac{21}{5}x-\frac{56}{5}+\frac{5}{3}x+\frac{1}{3}\left(-2\right)=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Multiply \frac{1}{3} and -2 to get \frac{-2}{3}.

$$\frac{21}{5}x-\frac{56}{5}+\frac{5}{3}x+\frac{-2}{3}=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{21}{5}x-\frac{56}{5}+\frac{5}{3}x-\frac{2}{3}=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Combine \frac{21}{5}x and \frac{5}{3}x to get \frac{88}{15}x.

$$\frac{88}{15}x-\frac{56}{5}-\frac{2}{3}=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Least common multiple of 5 and 3 is 15. Convert -\frac{56}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{88}{15}x-\frac{168}{15}-\frac{10}{15}=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Since -\frac{168}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{88}{15}x+\frac{-168-10}{15}=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Subtract 10 from -168 to get -178.

$$\frac{88}{15}x-\frac{178}{15}=\frac{1}{4}\left(x+4\right)+\frac{2}{3}\left(x-3\right)$$

Use the distributive property to multiply \frac{1}{4} by x+4.

$$\frac{88}{15}x-\frac{178}{15}=\frac{1}{4}x+\frac{1}{4}\times 4+\frac{2}{3}\left(x-3\right)$$

Cancel out 4 and 4.

$$\frac{88}{15}x-\frac{178}{15}=\frac{1}{4}x+1+\frac{2}{3}\left(x-3\right)$$

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

$$\frac{88}{15}x-\frac{178}{15}=\frac{1}{4}x+1+\frac{2}{3}x+\frac{2}{3}\left(-3\right)$$

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

$$\frac{88}{15}x-\frac{178}{15}=\frac{1}{4}x+1+\frac{2}{3}x+\frac{2\left(-3\right)}{3}$$

Multiply 2 and -3 to get -6.

$$\frac{88}{15}x-\frac{178}{15}=\frac{1}{4}x+1+\frac{2}{3}x+\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$\frac{88}{15}x-\frac{178}{15}=\frac{1}{4}x+1+\frac{2}{3}x-2$$

Combine \frac{1}{4}x and \frac{2}{3}x to get \frac{11}{12}x.

$$\frac{88}{15}x-\frac{178}{15}=\frac{11}{12}x+1-2$$

Subtract 2 from 1 to get -1.

$$\frac{88}{15}x-\frac{178}{15}=\frac{11}{12}x-1$$

Subtract \frac{11}{12}x from both sides.

$$\frac{88}{15}x-\frac{178}{15}-\frac{11}{12}x=-1$$

Combine \frac{88}{15}x and -\frac{11}{12}x to get \frac{99}{20}x.

$$\frac{99}{20}x-\frac{178}{15}=-1$$

Add \frac{178}{15} to both sides.

$$\frac{99}{20}x=-1+\frac{178}{15}$$

Convert -1 to fraction -\frac{15}{15}.

$$\frac{99}{20}x=-\frac{15}{15}+\frac{178}{15}$$

Since -\frac{15}{15} and \frac{178}{15} have the same denominator, add them by adding their numerators.

$$\frac{99}{20}x=\frac{-15+178}{15}$$

Add -15 and 178 to get 163.

$$\frac{99}{20}x=\frac{163}{15}$$

Multiply both sides by \frac{20}{99}, the reciprocal of \frac{99}{20}.

$$x=\frac{163}{15}\times \frac{20}{99}$$

Multiply \frac{163}{15} times \frac{20}{99} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{163\times 20}{15\times 99}$$

Do the multiplications in the fraction \frac{163\times 20}{15\times 99}.

$$x=\frac{3260}{1485}$$

Reduce the fraction \frac{3260}{1485} to lowest terms by extracting and canceling out 5.

$$x=\frac{652}{297}$$