Solve frac{28sqrt{3}-sqrt{3}x}{2}+1.5=x+17

$$\frac { 28 \sqrt { 3 } - \sqrt { 3 } x } { 2 } + 1.5 = x + 17$$

Solve for x

$$x=87\sqrt{3}-146\approx 4.688420258$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$28\sqrt{3}-\sqrt{3}x+3=2x+34$$

Subtract 2x from both sides.

$$28\sqrt{3}-\sqrt{3}x+3-2x=34$$

Subtract 3 from both sides.

$$28\sqrt{3}-\sqrt{3}x-2x=34-3$$

Subtract 3 from 34 to get 31.

$$28\sqrt{3}-\sqrt{3}x-2x=31$$

Subtract 28\sqrt{3} from both sides.

$$-\sqrt{3}x-2x=31-28\sqrt{3}$$

Combine all terms containing x.

$$\left(-\sqrt{3}-2\right)x=31-28\sqrt{3}$$

Divide both sides by -\sqrt{3}-2.

$$\frac{\left(-\sqrt{3}-2\right)x}{-\sqrt{3}-2}=\frac{31-28\sqrt{3}}{-\sqrt{3}-2}$$

Dividing by -\sqrt{3}-2 undoes the multiplication by -\sqrt{3}-2.

$$x=\frac{31-28\sqrt{3}}{-\sqrt{3}-2}$$

Divide 31-28\sqrt{3} by -\sqrt{3}-2.

$$x=87\sqrt{3}-146$$