Solve 2alpha-(11-2alpha)=5(2-alpha)-alpha-2(alpha-3)

$$2 \alpha - ( 11 - 2 \alpha ) = 5 ( 2 - \alpha ) - \alpha - 2 ( \alpha - 3 )$$

Solve for α

$$\alpha =\frac{9}{4}=2.25$$

Steps for Solving Linear Equation

To find the opposite of 11-2\alpha , find the opposite of each term.

$$2\alpha -11-\left(-2\alpha \right)=5\left(2-\alpha \right)-\alpha -2\left(\alpha -3\right)$$

The opposite of -2\alpha is 2\alpha .

$$2\alpha -11+2\alpha =5\left(2-\alpha \right)-\alpha -2\left(\alpha -3\right)$$

Combine 2\alpha and 2\alpha to get 4\alpha .

$$4\alpha -11=5\left(2-\alpha \right)-\alpha -2\left(\alpha -3\right)$$

Use the distributive property to multiply 5 by 2-\alpha .

$$4\alpha -11=10-5\alpha -\alpha -2\left(\alpha -3\right)$$

Combine -5\alpha and -\alpha to get -6\alpha .

$$4\alpha -11=10-6\alpha -2\left(\alpha -3\right)$$

Use the distributive property to multiply -2 by \alpha -3.

$$4\alpha -11=10-6\alpha -2\alpha +6$$

Combine -6\alpha and -2\alpha to get -8\alpha .

$$4\alpha -11=10-8\alpha +6$$

Add 10 and 6 to get 16.

$$4\alpha -11=16-8\alpha$$

Add 8\alpha to both sides.

$$4\alpha -11+8\alpha =16$$

Combine 4\alpha and 8\alpha to get 12\alpha .

$$12\alpha -11=16$$

Add 11 to both sides.

$$12\alpha =16+11$$

Add 16 and 11 to get 27.

$$12\alpha =27$$

Divide both sides by 12.

$$\alpha =\frac{27}{12}$$

Reduce the fraction \frac{27}{12} to lowest terms by extracting and canceling out 3.

$$\alpha =\frac{9}{4}$$