Solve 1/3(3a-1)+2/5(4a+3)-3/5(a-7)

$$\frac { 1 } { 3 } ( 3 a - 1 ) + \frac { 2 } { 5 } ( 4 a + 3 ) - \frac { 3 } { 5 } ( a - 7 )$$

Evaluate

$$2a+\frac{76}{15}$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by 3a-1.

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

Cancel out 3 and 3.

$$a+\frac{1}{3}\left(-1\right)+\frac{2}{5}\left(4a+3\right)-\frac{3}{5}\left(a-7\right)$$

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

$$a-\frac{1}{3}+\frac{2}{5}\left(4a+3\right)-\frac{3}{5}\left(a-7\right)$$

Use the distributive property to multiply \frac{2}{5} by 4a+3.

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

Express \frac{2}{5}\times 4 as a single fraction.

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

Multiply 2 and 4 to get 8.

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

Express \frac{2}{5}\times 3 as a single fraction.

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

Multiply 2 and 3 to get 6.

$$a-\frac{1}{3}+\frac{8}{5}a+\frac{6}{5}-\frac{3}{5}\left(a-7\right)$$

Combine a and \frac{8}{5}a to get \frac{13}{5}a.

$$\frac{13}{5}a-\frac{1}{3}+\frac{6}{5}-\frac{3}{5}\left(a-7\right)$$

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{6}{5} to fractions with denominator 15.

$$\frac{13}{5}a-\frac{5}{15}+\frac{18}{15}-\frac{3}{5}\left(a-7\right)$$

Since -\frac{5}{15} and \frac{18}{15} have the same denominator, add them by adding their numerators.

$$\frac{13}{5}a+\frac{-5+18}{15}-\frac{3}{5}\left(a-7\right)$$

Add -5 and 18 to get 13.

$$\frac{13}{5}a+\frac{13}{15}-\frac{3}{5}\left(a-7\right)$$

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

$$\frac{13}{5}a+\frac{13}{15}-\frac{3}{5}a-\frac{3}{5}\left(-7\right)$$

Express -\frac{3}{5}\left(-7\right) as a single fraction.

$$\frac{13}{5}a+\frac{13}{15}-\frac{3}{5}a+\frac{-3\left(-7\right)}{5}$$

Multiply -3 and -7 to get 21.

$$\frac{13}{5}a+\frac{13}{15}-\frac{3}{5}a+\frac{21}{5}$$

Combine \frac{13}{5}a and -\frac{3}{5}a to get 2a.

$$2a+\frac{13}{15}+\frac{21}{5}$$

Least common multiple of 15 and 5 is 15. Convert \frac{13}{15} and \frac{21}{5} to fractions with denominator 15.

$$2a+\frac{13}{15}+\frac{63}{15}$$

Since \frac{13}{15} and \frac{63}{15} have the same denominator, add them by adding their numerators.

$$2a+\frac{13+63}{15}$$

Add 13 and 63 to get 76.

$$2a+\frac{76}{15}$$

Expand

$$2a+\frac{76}{15}$$

Solution Steps

Use the distributive property to multiply \frac{1}{3} by 3a-1.

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

Cancel out 3 and 3.

$$a+\frac{1}{3}\left(-1\right)+\frac{2}{5}\left(4a+3\right)-\frac{3}{5}\left(a-7\right)$$

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

$$a-\frac{1}{3}+\frac{2}{5}\left(4a+3\right)-\frac{3}{5}\left(a-7\right)$$

Use the distributive property to multiply \frac{2}{5} by 4a+3.

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

Express \frac{2}{5}\times 4 as a single fraction.

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

Multiply 2 and 4 to get 8.

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

Express \frac{2}{5}\times 3 as a single fraction.

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

Multiply 2 and 3 to get 6.

$$a-\frac{1}{3}+\frac{8}{5}a+\frac{6}{5}-\frac{3}{5}\left(a-7\right)$$

Combine a and \frac{8}{5}a to get \frac{13}{5}a.

$$\frac{13}{5}a-\frac{1}{3}+\frac{6}{5}-\frac{3}{5}\left(a-7\right)$$

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{6}{5} to fractions with denominator 15.

$$\frac{13}{5}a-\frac{5}{15}+\frac{18}{15}-\frac{3}{5}\left(a-7\right)$$

Since -\frac{5}{15} and \frac{18}{15} have the same denominator, add them by adding their numerators.

$$\frac{13}{5}a+\frac{-5+18}{15}-\frac{3}{5}\left(a-7\right)$$

Add -5 and 18 to get 13.

$$\frac{13}{5}a+\frac{13}{15}-\frac{3}{5}\left(a-7\right)$$

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

$$\frac{13}{5}a+\frac{13}{15}-\frac{3}{5}a-\frac{3}{5}\left(-7\right)$$

Express -\frac{3}{5}\left(-7\right) as a single fraction.

$$\frac{13}{5}a+\frac{13}{15}-\frac{3}{5}a+\frac{-3\left(-7\right)}{5}$$

Multiply -3 and -7 to get 21.

$$\frac{13}{5}a+\frac{13}{15}-\frac{3}{5}a+\frac{21}{5}$$

Combine \frac{13}{5}a and -\frac{3}{5}a to get 2a.

$$2a+\frac{13}{15}+\frac{21}{5}$$

Least common multiple of 15 and 5 is 15. Convert \frac{13}{15} and \frac{21}{5} to fractions with denominator 15.

$$2a+\frac{13}{15}+\frac{63}{15}$$

Since \frac{13}{15} and \frac{63}{15} have the same denominator, add them by adding their numerators.

$$2a+\frac{13+63}{15}$$

Add 13 and 63 to get 76.

$$2a+\frac{76}{15}$$