Solve 4/5(x+3)+7/10(x-2)=4/15(x-3)

$$\frac { 4 } { 5 } ( x + 3 ) + \frac { 7 } { 10 } ( x - 2 ) = \frac { 4 } { 15 } ( x - 3 )$$

Solve for x

$$x = -\frac{54}{37} = -1\frac{17}{37} \approx -1.459459459$$

Steps for Solving Linear Equation

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

$$\frac{4}{5}x+\frac{4}{5}\times 3+\frac{7}{10}\left(x-2\right)=\frac{4}{15}\left(x-3\right)$$

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

$$\frac{4}{5}x+\frac{4\times 3}{5}+\frac{7}{10}\left(x-2\right)=\frac{4}{15}\left(x-3\right)$$

Multiply 4 and 3 to get 12.

$$\frac{4}{5}x+\frac{12}{5}+\frac{7}{10}\left(x-2\right)=\frac{4}{15}\left(x-3\right)$$

Use the distributive property to multiply \frac{7}{10} by x-2.

$$\frac{4}{5}x+\frac{12}{5}+\frac{7}{10}x+\frac{7}{10}\left(-2\right)=\frac{4}{15}\left(x-3\right)$$

Express \frac{7}{10}\left(-2\right) as a single fraction.

$$\frac{4}{5}x+\frac{12}{5}+\frac{7}{10}x+\frac{7\left(-2\right)}{10}=\frac{4}{15}\left(x-3\right)$$

Multiply 7 and -2 to get -14.

$$\frac{4}{5}x+\frac{12}{5}+\frac{7}{10}x+\frac{-14}{10}=\frac{4}{15}\left(x-3\right)$$

Reduce the fraction \frac{-14}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}x+\frac{12}{5}+\frac{7}{10}x-\frac{7}{5}=\frac{4}{15}\left(x-3\right)$$

Combine \frac{4}{5}x and \frac{7}{10}x to get \frac{3}{2}x.

$$\frac{3}{2}x+\frac{12}{5}-\frac{7}{5}=\frac{4}{15}\left(x-3\right)$$

Since \frac{12}{5} and \frac{7}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}x+\frac{12-7}{5}=\frac{4}{15}\left(x-3\right)$$

Subtract 7 from 12 to get 5.

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

Divide 5 by 5 to get 1.

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

Use the distributive property to multiply \frac{4}{15} by x-3.

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

Express \frac{4}{15}\left(-3\right) as a single fraction.

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

Multiply 4 and -3 to get -12.

$$\frac{3}{2}x+1=\frac{4}{15}x+\frac{-12}{15}$$

Reduce the fraction \frac{-12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{3}{2}x+1=\frac{4}{15}x-\frac{4}{5}$$

Subtract \frac{4}{15}x from both sides.

$$\frac{3}{2}x+1-\frac{4}{15}x=-\frac{4}{5}$$

Combine \frac{3}{2}x and -\frac{4}{15}x to get \frac{37}{30}x.

$$\frac{37}{30}x+1=-\frac{4}{5}$$

Subtract 1 from both sides.

$$\frac{37}{30}x=-\frac{4}{5}-1$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{37}{30}x=-\frac{4}{5}-\frac{5}{5}$$

Since -\frac{4}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{37}{30}x=\frac{-4-5}{5}$$

Subtract 5 from -4 to get -9.

$$\frac{37}{30}x=-\frac{9}{5}$$

Multiply both sides by \frac{30}{37}, the reciprocal of \frac{37}{30}.

$$x=-\frac{9}{5}\times \frac{30}{37}$$

Multiply -\frac{9}{5} times \frac{30}{37} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\times 30}{5\times 37}$$

Do the multiplications in the fraction \frac{-9\times 30}{5\times 37}.

$$x=\frac{-270}{185}$$

Reduce the fraction \frac{-270}{185} to lowest terms by extracting and canceling out 5.

$$x=-\frac{54}{37}$$