Solve (1/3(3x-10-7x/2)-1/2(2x-2x+2/3)-frac{x}{2}-1

$$( \frac { 1 } { 3 } ( 3 x - \frac { 10 - 7 x } { 2 } ) - \frac { 1 } { 2 } ( 2 x - \frac { 2 x + 2 } { 3 } ) - \frac { x } { 2 } - 1$$

Evaluate

$$x = -\frac{7}{3} = -2\frac{1}{3} = -2.3333333333333335$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{2}{2}.

$$\frac{1}{3}\left(\frac{2\times 3x}{2}-\frac{10-7x}{2}\right)-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Since \frac{2\times 3x}{2} and \frac{10-7x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{2\times 3x-\left(10-7x\right)}{2}-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Do the multiplications in 2\times 3x-\left(10-7x\right).

$$\frac{1}{3}\times \frac{6x-10+7x}{2}-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Combine like terms in 6x-10+7x.

$$\frac{1}{3}\times \frac{13x-10}{2}-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Multiply \frac{1}{3} times \frac{13x-10}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{3}{3}.

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\left(\frac{3\times 2x}{3}-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Since \frac{3\times 2x}{3} and \frac{2x+2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\times \frac{3\times 2x-\left(2x+2\right)}{3}-\frac{x}{2}-1$$

Do the multiplications in 3\times 2x-\left(2x+2\right).

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\times \frac{6x-2x-2}{3}-\frac{x}{2}-1$$

Combine like terms in 6x-2x-2.

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\times \frac{4x-2}{3}-\frac{x}{2}-1$$

Multiply \frac{1}{2} times \frac{4x-2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13x-10}{3\times 2}-\frac{4x-2}{2\times 3}-\frac{x}{2}-1$$

Multiply 2 and 3 to get 6.

$$\frac{13x-10}{3\times 2}-\frac{4x-2}{6}-\frac{x}{2}-1$$

To add or subtract expressions, expand them to make their denominators the same. Expand 3\times 2.

$$\frac{13x-10}{6}-\frac{4x-2}{6}-\frac{x}{2}-1$$

Since \frac{13x-10}{6} and \frac{4x-2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13x-10-\left(4x-2\right)}{6}-\frac{x}{2}-1$$

Do the multiplications in 13x-10-\left(4x-2\right).

$$\frac{13x-10-4x+2}{6}-\frac{x}{2}-1$$

Combine like terms in 13x-10-4x+2.

$$\frac{9x-8}{6}-\frac{x}{2}-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 2 is 6. Multiply \frac{x}{2} times \frac{3}{3}.

$$\frac{9x-8}{6}-\frac{3x}{6}-1$$

Since \frac{9x-8}{6} and \frac{3x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9x-8-3x}{6}-1$$

Combine like terms in 9x-8-3x.

$$\frac{6x-8}{6}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6}{6}.

$$\frac{6x-8}{6}-\frac{6}{6}$$

Since \frac{6x-8}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6x-8-6}{6}$$

Combine like terms in 6x-8-6.

$$\frac{6x-14}{6}$$

Expand

$$x = -\frac{7}{3} = -2\frac{1}{3} = -2.3333333333333335$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{2}{2}.

$$\frac{1}{3}\left(\frac{2\times 3x}{2}-\frac{10-7x}{2}\right)-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Since \frac{2\times 3x}{2} and \frac{10-7x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{2\times 3x-\left(10-7x\right)}{2}-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Do the multiplications in 2\times 3x-\left(10-7x\right).

$$\frac{1}{3}\times \frac{6x-10+7x}{2}-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Combine like terms in 6x-10+7x.

$$\frac{1}{3}\times \frac{13x-10}{2}-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Multiply \frac{1}{3} times \frac{13x-10}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\left(2x-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{3}{3}.

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\left(\frac{3\times 2x}{3}-\frac{2x+2}{3}\right)-\frac{x}{2}-1$$

Since \frac{3\times 2x}{3} and \frac{2x+2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\times \frac{3\times 2x-\left(2x+2\right)}{3}-\frac{x}{2}-1$$

Do the multiplications in 3\times 2x-\left(2x+2\right).

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\times \frac{6x-2x-2}{3}-\frac{x}{2}-1$$

Combine like terms in 6x-2x-2.

$$\frac{13x-10}{3\times 2}-\frac{1}{2}\times \frac{4x-2}{3}-\frac{x}{2}-1$$

Multiply \frac{1}{2} times \frac{4x-2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13x-10}{3\times 2}-\frac{4x-2}{2\times 3}-\frac{x}{2}-1$$

Multiply 2 and 3 to get 6.

$$\frac{13x-10}{3\times 2}-\frac{4x-2}{6}-\frac{x}{2}-1$$

To add or subtract expressions, expand them to make their denominators the same. Expand 3\times 2.

$$\frac{13x-10}{6}-\frac{4x-2}{6}-\frac{x}{2}-1$$

Since \frac{13x-10}{6} and \frac{4x-2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13x-10-\left(4x-2\right)}{6}-\frac{x}{2}-1$$

Do the multiplications in 13x-10-\left(4x-2\right).

$$\frac{13x-10-4x+2}{6}-\frac{x}{2}-1$$

Combine like terms in 13x-10-4x+2.

$$\frac{9x-8}{6}-\frac{x}{2}-1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 2 is 6. Multiply \frac{x}{2} times \frac{3}{3}.

$$\frac{9x-8}{6}-\frac{3x}{6}-1$$

Since \frac{9x-8}{6} and \frac{3x}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9x-8-3x}{6}-1$$

Combine like terms in 9x-8-3x.

$$\frac{6x-8}{6}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{6}{6}.

$$\frac{6x-8}{6}-\frac{6}{6}$$

Since \frac{6x-8}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6x-8-6}{6}$$

Combine like terms in 6x-8-6.

$$\frac{6x-14}{6}$$