Solve 4+2sqrt{3}+2sqrt{3}+3=x+bsqrt{3}

$$4+2 \sqrt{ 3 } +2 \sqrt{ 3 } +3 = x+b \sqrt{ 3 }$$

Solve for b

$$b=-\frac{\sqrt{3}\left(x-4\sqrt{3}-7\right)}{3}$$

Steps for Solving Linear Equation

Combine 2\sqrt{3} and 2\sqrt{3} to get 4\sqrt{3}.

$$4+4\sqrt{3}+3=x+b\sqrt{3}$$

Add 4 and 3 to get 7.

$$7+4\sqrt{3}=x+b\sqrt{3}$$

Swap sides so that all variable terms are on the left hand side.

$$x+b\sqrt{3}=7+4\sqrt{3}$$

Subtract x from both sides.

$$b\sqrt{3}=7+4\sqrt{3}-x$$

The equation is in standard form.

$$\sqrt{3}b=-x+4\sqrt{3}+7$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}b}{\sqrt{3}}=\frac{-x+4\sqrt{3}+7}{\sqrt{3}}$$

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

$$b=\frac{-x+4\sqrt{3}+7}{\sqrt{3}}$$

Divide 7+4\sqrt{3}-x by \sqrt{3}.

$$b=\frac{\sqrt{3}\left(-x+4\sqrt{3}+7\right)}{3}$$

Solve for x

$$x=\sqrt{3}\left(4-b\right)+7$$