Solve 2-3(sqrt{3}+x)=4(2sqrt{3}-x)

$$2 - 3 ( \sqrt { 3 } + x ) = 4 ( 2 \sqrt { 3 } - x )$$

Solve for x

$$x=11\sqrt{3}-2\approx 17.052558883$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by \sqrt{3}+x.

$$2-3\sqrt{3}-3x=4\left(2\sqrt{3}-x\right)$$

Use the distributive property to multiply 4 by 2\sqrt{3}-x.

$$2-3\sqrt{3}-3x=8\sqrt{3}-4x$$

Add 4x to both sides.

$$2-3\sqrt{3}-3x+4x=8\sqrt{3}$$

Combine -3x and 4x to get x.

$$2-3\sqrt{3}+x=8\sqrt{3}$$

Subtract 2 from both sides.

$$-3\sqrt{3}+x=8\sqrt{3}-2$$

Add 3\sqrt{3} to both sides.

$$x=8\sqrt{3}-2+3\sqrt{3}$$

Combine 8\sqrt{3} and 3\sqrt{3} to get 11\sqrt{3}.

$$x=11\sqrt{3}-2$$