Solve 15(3x-2)-7(2x-1)-[17/5(2x/7+7/1)-7(x-7)]

$$15 ( 3 x - 2 ) - 7 ( 2 x - 1 ) - [ \frac { 17 } { 5 } ( \frac { 2 x } { 7 } + \frac { 7 } { 1 } ) - 7 ( x - 7 ) ]$$

Evaluate

$$\frac{1296x}{35}-\frac{479}{5}$$

Short Solution Steps

Anything divided by one gives itself.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17}{5}\left(\frac{2x}{7}+7\right)-7\left(x-7\right)\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{7}{7}.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17}{5}\left(\frac{2x}{7}+\frac{7\times 7}{7}\right)-7\left(x-7\right)\right)$$

Since \frac{2x}{7} and \frac{7\times 7}{7} have the same denominator, add them by adding their numerators.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17}{5}\times \frac{2x+7\times 7}{7}-7\left(x-7\right)\right)$$

Do the multiplications in 2x+7\times 7.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17}{5}\times \frac{2x+49}{7}-7\left(x-7\right)\right)$$

Multiply \frac{17}{5} times \frac{2x+49}{7} by multiplying numerator times numerator and denominator times denominator.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17\left(2x+49\right)}{5\times 7}-7\left(x-7\right)\right)$$

To find the opposite of \frac{17\left(2x+49\right)}{5\times 7}-7\left(x-7\right), find the opposite of each term.

$$15\left(3x-2\right)-7\left(2x-1\right)-\frac{17\left(2x+49\right)}{5\times 7}-\left(-7\left(x-7\right)\right)$$

Multiply 5 and 7 to get 35.

$$15\left(3x-2\right)-7\left(2x-1\right)-\frac{17\left(2x+49\right)}{35}-\left(-7\left(x-7\right)\right)$$

The opposite of -7\left(x-7\right) is 7\left(x-7\right).

$$15\left(3x-2\right)-7\left(2x-1\right)-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Use the distributive property to multiply 15 by 3x-2.

$$45x-30-7\left(2x-1\right)-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Use the distributive property to multiply -7 by 2x-1.

$$45x-30-14x+7-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Combine 45x and -14x to get 31x.

$$31x-30+7-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Add -30 and 7 to get -23.

$$31x-23-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Use the distributive property to multiply 17 by 2x+49.

$$31x-23-\frac{34x+833}{35}+7\left(x-7\right)$$

Use the distributive property to multiply 7 by x-7.

$$31x-23-\frac{34x+833}{35}+7x-49$$

Combine 31x and 7x to get 38x.

$$38x-23-\frac{34x+833}{35}-49$$

Subtract 49 from -23 to get -72.

$$38x-72-\frac{34x+833}{35}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 38x-72 times \frac{35}{35}.

$$\frac{35\left(38x-72\right)}{35}-\frac{34x+833}{35}$$

Since \frac{35\left(38x-72\right)}{35} and \frac{34x+833}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35\left(38x-72\right)-\left(34x+833\right)}{35}$$

Do the multiplications in 35\left(38x-72\right)-\left(34x+833\right).

$$\frac{1330x-2520-34x-833}{35}$$

Combine like terms in 1330x-2520-34x-833.

$$\frac{1296x-3353}{35}$$

Expand

$$\frac{1296x}{35}-\frac{479}{5}$$

Short Solution Steps

Anything divided by one gives itself.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17}{5}\left(\frac{2x}{7}+7\right)-7\left(x-7\right)\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{7}{7}.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17}{5}\left(\frac{2x}{7}+\frac{7\times 7}{7}\right)-7\left(x-7\right)\right)$$

Since \frac{2x}{7} and \frac{7\times 7}{7} have the same denominator, add them by adding their numerators.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17}{5}\times \frac{2x+7\times 7}{7}-7\left(x-7\right)\right)$$

Do the multiplications in 2x+7\times 7.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17}{5}\times \frac{2x+49}{7}-7\left(x-7\right)\right)$$

Multiply \frac{17}{5} times \frac{2x+49}{7} by multiplying numerator times numerator and denominator times denominator.

$$15\left(3x-2\right)-7\left(2x-1\right)-\left(\frac{17\left(2x+49\right)}{5\times 7}-7\left(x-7\right)\right)$$

To find the opposite of \frac{17\left(2x+49\right)}{5\times 7}-7\left(x-7\right), find the opposite of each term.

$$15\left(3x-2\right)-7\left(2x-1\right)-\frac{17\left(2x+49\right)}{5\times 7}-\left(-7\left(x-7\right)\right)$$

Multiply 5 and 7 to get 35.

$$15\left(3x-2\right)-7\left(2x-1\right)-\frac{17\left(2x+49\right)}{35}-\left(-7\left(x-7\right)\right)$$

The opposite of -7\left(x-7\right) is 7\left(x-7\right).

$$15\left(3x-2\right)-7\left(2x-1\right)-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Use the distributive property to multiply 15 by 3x-2.

$$45x-30-7\left(2x-1\right)-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Use the distributive property to multiply -7 by 2x-1.

$$45x-30-14x+7-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Combine 45x and -14x to get 31x.

$$31x-30+7-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Add -30 and 7 to get -23.

$$31x-23-\frac{17\left(2x+49\right)}{35}+7\left(x-7\right)$$

Use the distributive property to multiply 17 by 2x+49.

$$31x-23-\frac{34x+833}{35}+7\left(x-7\right)$$

Use the distributive property to multiply 7 by x-7.

$$31x-23-\frac{34x+833}{35}+7x-49$$

Combine 31x and 7x to get 38x.

$$38x-23-\frac{34x+833}{35}-49$$

Subtract 49 from -23 to get -72.

$$38x-72-\frac{34x+833}{35}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 38x-72 times \frac{35}{35}.

$$\frac{35\left(38x-72\right)}{35}-\frac{34x+833}{35}$$

Since \frac{35\left(38x-72\right)}{35} and \frac{34x+833}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35\left(38x-72\right)-\left(34x+833\right)}{35}$$

Do the multiplications in 35\left(38x-72\right)-\left(34x+833\right).

$$\frac{1330x-2520-34x-833}{35}$$

Combine like terms in 1330x-2520-34x-833.

$$\frac{1296x-3353}{35}$$