Solve 10(x/2-6)-3(x-8)-4(x-3)

$$10 ( \frac { x } { 2 } - 6 ) - 3 ( x - 8 ) - 4 ( x - 3 )$$

Evaluate

$$-2x-24$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{2}{2}.

$$10\left(\frac{x}{2}-\frac{6\times 2}{2}\right)-3\left(x-8\right)-4\left(x-3\right)$$

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

$$10\times \frac{x-6\times 2}{2}-3\left(x-8\right)-4\left(x-3\right)$$

Do the multiplications in x-6\times 2.

$$10\times \frac{x-12}{2}-3\left(x-8\right)-4\left(x-3\right)$$

Cancel out 2, the greatest common factor in 10 and 2.

$$5\left(x-12\right)-3\left(x-8\right)-4\left(x-3\right)$$

Use the distributive property to multiply 5 by x-12.

$$5x-60-3\left(x-8\right)-4\left(x-3\right)$$

Use the distributive property to multiply -3 by x-8.

$$5x-60-3x+24-4\left(x-3\right)$$

Combine 5x and -3x to get 2x.

$$2x-60+24-4\left(x-3\right)$$

Add -60 and 24 to get -36.

$$2x-36-4\left(x-3\right)$$

Use the distributive property to multiply -4 by x-3.

$$2x-36-4x+12$$

Combine 2x and -4x to get -2x.

$$-2x-36+12$$

Add -36 and 12 to get -24.

$$-2x-24$$

Expand

$$-2x-24$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{2}{2}.

$$10\left(\frac{x}{2}-\frac{6\times 2}{2}\right)-3\left(x-8\right)-4\left(x-3\right)$$

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

$$10\times \frac{x-6\times 2}{2}-3\left(x-8\right)-4\left(x-3\right)$$

Do the multiplications in x-6\times 2.

$$10\times \frac{x-12}{2}-3\left(x-8\right)-4\left(x-3\right)$$

Cancel out 2, the greatest common factor in 10 and 2.

$$5\left(x-12\right)-3\left(x-8\right)-4\left(x-3\right)$$

Use the distributive property to multiply 5 by x-12.

$$5x-60-3\left(x-8\right)-4\left(x-3\right)$$

Use the distributive property to multiply -3 by x-8.

$$5x-60-3x+24-4\left(x-3\right)$$

Combine 5x and -3x to get 2x.

$$2x-60+24-4\left(x-3\right)$$

Add -60 and 24 to get -36.

$$2x-36-4\left(x-3\right)$$

Use the distributive property to multiply -4 by x-3.

$$2x-36-4x+12$$

Combine 2x and -4x to get -2x.

$$-2x-36+12$$

Add -36 and 12 to get -24.

$$-2x-24$$