Solve (x+y-2)-7/2(2x-y-1)

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

Evaluate

$$\frac{9y}{2}-6x+\frac{3}{2}$$

Solution Steps

Use the distributive property to multiply -\frac{7}{2} by 2x-y-1.

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

Cancel out 2 and 2.

$$x+y-2-7x-\frac{7}{2}\left(-1\right)y-\frac{7}{2}\left(-1\right)$$

Multiply -\frac{7}{2} and -1 to get \frac{7}{2}.

$$x+y-2-7x+\frac{7}{2}y-\frac{7}{2}\left(-1\right)$$

Multiply -\frac{7}{2} and -1 to get \frac{7}{2}.

$$x+y-2-7x+\frac{7}{2}y+\frac{7}{2}$$

Combine x and -7x to get -6x.

$$-6x+y-2+\frac{7}{2}y+\frac{7}{2}$$

Combine y and \frac{7}{2}y to get \frac{9}{2}y.

$$-6x+\frac{9}{2}y-2+\frac{7}{2}$$

Convert -2 to fraction -\frac{4}{2}.

$$-6x+\frac{9}{2}y-\frac{4}{2}+\frac{7}{2}$$

Since -\frac{4}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$-6x+\frac{9}{2}y+\frac{-4+7}{2}$$

Add -4 and 7 to get 3.

$$-6x+\frac{9}{2}y+\frac{3}{2}$$

Expand

$$\frac{9y}{2}-6x+\frac{3}{2}$$

Solution Steps

Use the distributive property to multiply -\frac{7}{2} by 2x-y-1.

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

Cancel out 2 and 2.

$$x+y-2-7x-\frac{7}{2}\left(-1\right)y-\frac{7}{2}\left(-1\right)$$

Multiply -\frac{7}{2} and -1 to get \frac{7}{2}.

$$x+y-2-7x+\frac{7}{2}y-\frac{7}{2}\left(-1\right)$$

Multiply -\frac{7}{2} and -1 to get \frac{7}{2}.

$$x+y-2-7x+\frac{7}{2}y+\frac{7}{2}$$

Combine x and -7x to get -6x.

$$-6x+y-2+\frac{7}{2}y+\frac{7}{2}$$

Combine y and \frac{7}{2}y to get \frac{9}{2}y.

$$-6x+\frac{9}{2}y-2+\frac{7}{2}$$

Convert -2 to fraction -\frac{4}{2}.

$$-6x+\frac{9}{2}y-\frac{4}{2}+\frac{7}{2}$$

Since -\frac{4}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$-6x+\frac{9}{2}y+\frac{-4+7}{2}$$

Add -4 and 7 to get 3.

$$-6x+\frac{9}{2}y+\frac{3}{2}$$