Solve a-3/a-2-x+4/2*1=5

$$\frac { a - 3 } { a - 2 } - \frac { x + 4 } { 2 \cdot 1 } = 5$$

Solve for a

$$a=\frac{2\left(x+11\right)}{x+12}$$

$$x\neq -12$$

Steps for Solving Linear Equation

Variable a cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by a-2.

$$a-3-\left(\frac{1}{2}a-1\right)\left(x+4\right)=5\left(a-2\right)$$

Use the distributive property to multiply \frac{1}{2}a-1 by x+4.

$$a-3-\left(\frac{1}{2}ax+2a-x-4\right)=5\left(a-2\right)$$

To find the opposite of \frac{1}{2}ax+2a-x-4, find the opposite of each term.

$$a-3-\frac{1}{2}ax-2a+x+4=5\left(a-2\right)$$

Combine a and -2a to get -a.

$$-a-3-\frac{1}{2}ax+x+4=5\left(a-2\right)$$

Add -3 and 4 to get 1.

$$-a+1-\frac{1}{2}ax+x=5\left(a-2\right)$$

Use the distributive property to multiply 5 by a-2.

$$-a+1-\frac{1}{2}ax+x=5a-10$$

Subtract 5a from both sides.

$$-a+1-\frac{1}{2}ax+x-5a=-10$$

Combine -a and -5a to get -6a.

$$-6a+1-\frac{1}{2}ax+x=-10$$

Subtract 1 from both sides.

$$-6a-\frac{1}{2}ax+x=-10-1$$

Subtract 1 from -10 to get -11.

$$-6a-\frac{1}{2}ax+x=-11$$

Subtract x from both sides.

$$-6a-\frac{1}{2}ax=-11-x$$

Combine all terms containing a.

$$\left(-6-\frac{1}{2}x\right)a=-11-x$$

The equation is in standard form.

$$\left(-\frac{x}{2}-6\right)a=-x-11$$

Divide both sides by -6-\frac{1}{2}x.

$$\frac{\left(-\frac{x}{2}-6\right)a}{-\frac{x}{2}-6}=\frac{-x-11}{-\frac{x}{2}-6}$$

Dividing by -6-\frac{1}{2}x undoes the multiplication by -6-\frac{1}{2}x.

$$a=\frac{-x-11}{-\frac{x}{2}-6}$$

Divide -11-x by -6-\frac{1}{2}x.

$$a=\frac{2\left(x+11\right)}{x+12}$$

Variable a cannot be equal to 2.

$$a=\frac{2\left(x+11\right)}{x+12}\text{, }a\neq 2$$

Solve for x

$$x=-\frac{2\left(11-6a\right)}{2-a}$$

$$a\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a-2.

$$a-3-\left(\frac{1}{2}a-1\right)\left(x+4\right)=5\left(a-2\right)$$

Use the distributive property to multiply \frac{1}{2}a-1 by x+4.

$$a-3-\left(\frac{1}{2}ax+2a-x-4\right)=5\left(a-2\right)$$

To find the opposite of \frac{1}{2}ax+2a-x-4, find the opposite of each term.

$$a-3-\frac{1}{2}ax-2a+x+4=5\left(a-2\right)$$

Combine a and -2a to get -a.

$$-a-3-\frac{1}{2}ax+x+4=5\left(a-2\right)$$

Add -3 and 4 to get 1.

$$-a+1-\frac{1}{2}ax+x=5\left(a-2\right)$$

Use the distributive property to multiply 5 by a-2.

$$-a+1-\frac{1}{2}ax+x=5a-10$$

Add a to both sides.

$$1-\frac{1}{2}ax+x=5a-10+a$$

Combine 5a and a to get 6a.

$$1-\frac{1}{2}ax+x=6a-10$$

Subtract 1 from both sides.

$$-\frac{1}{2}ax+x=6a-10-1$$

Subtract 1 from -10 to get -11.

$$-\frac{1}{2}ax+x=6a-11$$

Combine all terms containing x.

$$\left(-\frac{1}{2}a+1\right)x=6a-11$$

The equation is in standard form.

$$\left(-\frac{a}{2}+1\right)x=6a-11$$

Divide both sides by -\frac{1}{2}a+1.

$$\frac{\left(-\frac{a}{2}+1\right)x}{-\frac{a}{2}+1}=\frac{6a-11}{-\frac{a}{2}+1}$$

Dividing by -\frac{1}{2}a+1 undoes the multiplication by -\frac{1}{2}a+1.

$$x=\frac{6a-11}{-\frac{a}{2}+1}$$

Divide 6a-11 by -\frac{1}{2}a+1.

$$x=\frac{2\left(6a-11\right)}{2-a}$$