Solve 2(1-3x)/5-2+3x/10-7-3(2x+1)/4

$$\frac { 2 ( 1 - 3 x ) } { 5 } - \frac { 2 + 3 x } { 10 } - 7 - \frac { 3 ( 2 x + 1 ) } { 4 }$$

Evaluate

$$-3x-\frac{151}{20}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 10 is 10. Multiply \frac{2\left(1-3x\right)}{5} times \frac{2}{2}.

$$\frac{2\times 2\left(1-3x\right)}{10}-\frac{2+3x}{10}-7-\frac{3\left(2x+1\right)}{4}$$

Since \frac{2\times 2\left(1-3x\right)}{10} and \frac{2+3x}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2\left(1-3x\right)-\left(2+3x\right)}{10}-7-\frac{3\left(2x+1\right)}{4}$$

Do the multiplications in 2\times 2\left(1-3x\right)-\left(2+3x\right).

$$\frac{4-12x-2-3x}{10}-7-\frac{3\left(2x+1\right)}{4}$$

Combine like terms in 4-12x-2-3x.

$$\frac{2-15x}{10}-7-\frac{3\left(2x+1\right)}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{10}{10}.

$$\frac{2-15x}{10}-\frac{7\times 10}{10}-\frac{3\left(2x+1\right)}{4}$$

Since \frac{2-15x}{10} and \frac{7\times 10}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-15x-7\times 10}{10}-\frac{3\left(2x+1\right)}{4}$$

Do the multiplications in 2-15x-7\times 10.

$$\frac{2-15x-70}{10}-\frac{3\left(2x+1\right)}{4}$$

Combine like terms in 2-15x-70.

$$\frac{-68-15x}{10}-\frac{3\left(2x+1\right)}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 4 is 20. Multiply \frac{-68-15x}{10} times \frac{2}{2}. Multiply \frac{3\left(2x+1\right)}{4} times \frac{5}{5}.

$$\frac{2\left(-68-15x\right)}{20}-\frac{5\times 3\left(2x+1\right)}{20}$$

Since \frac{2\left(-68-15x\right)}{20} and \frac{5\times 3\left(2x+1\right)}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-68-15x\right)-5\times 3\left(2x+1\right)}{20}$$

Do the multiplications in 2\left(-68-15x\right)-5\times 3\left(2x+1\right).

$$\frac{-136-30x-30x-15}{20}$$

Combine like terms in -136-30x-30x-15.

$$\frac{-151-60x}{20}$$

Expand

$$-3x-\frac{151}{20}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 10 is 10. Multiply \frac{2\left(1-3x\right)}{5} times \frac{2}{2}.

$$\frac{2\times 2\left(1-3x\right)}{10}-\frac{2+3x}{10}-7-\frac{3\left(2x+1\right)}{4}$$

Since \frac{2\times 2\left(1-3x\right)}{10} and \frac{2+3x}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 2\left(1-3x\right)-\left(2+3x\right)}{10}-7-\frac{3\left(2x+1\right)}{4}$$

Do the multiplications in 2\times 2\left(1-3x\right)-\left(2+3x\right).

$$\frac{4-12x-2-3x}{10}-7-\frac{3\left(2x+1\right)}{4}$$

Combine like terms in 4-12x-2-3x.

$$\frac{2-15x}{10}-7-\frac{3\left(2x+1\right)}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{10}{10}.

$$\frac{2-15x}{10}-\frac{7\times 10}{10}-\frac{3\left(2x+1\right)}{4}$$

Since \frac{2-15x}{10} and \frac{7\times 10}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-15x-7\times 10}{10}-\frac{3\left(2x+1\right)}{4}$$

Do the multiplications in 2-15x-7\times 10.

$$\frac{2-15x-70}{10}-\frac{3\left(2x+1\right)}{4}$$

Combine like terms in 2-15x-70.

$$\frac{-68-15x}{10}-\frac{3\left(2x+1\right)}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 4 is 20. Multiply \frac{-68-15x}{10} times \frac{2}{2}. Multiply \frac{3\left(2x+1\right)}{4} times \frac{5}{5}.

$$\frac{2\left(-68-15x\right)}{20}-\frac{5\times 3\left(2x+1\right)}{20}$$

Since \frac{2\left(-68-15x\right)}{20} and \frac{5\times 3\left(2x+1\right)}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(-68-15x\right)-5\times 3\left(2x+1\right)}{20}$$

Do the multiplications in 2\left(-68-15x\right)-5\times 3\left(2x+1\right).

$$\frac{-136-30x-30x-15}{20}$$

Combine like terms in -136-30x-30x-15.

$$\frac{-151-60x}{20}$$