Solve 1/2x-1/2=5-1/2x-x22sqrt[6]{6}

$$\frac{ 1 }{ 2 } x- \frac{ 1 }{ 2 } = 5- \frac{ 1 }{ 2 } x-x22 \sqrt[ 6 ]{ 6 }$$

Solve for x

$$x=-\sqrt[6]{6}x_{22}+\frac{11}{2}$$

Solution Steps

Subtract 5-\frac{1}{2}x from both sides.

$$\frac{1}{2}x-\frac{1}{2}-\left(5-\frac{1}{2}x\right)=-x_{22}\sqrt[6]{6}$$

To find the opposite of 5-\frac{1}{2}x, find the opposite of each term.

$$\frac{1}{2}x-\frac{1}{2}-5+\frac{1}{2}x=-x_{22}\sqrt[6]{6}$$

Subtract 5 from -\frac{1}{2} to get -\frac{11}{2}.

$$\frac{1}{2}x-\frac{11}{2}+\frac{1}{2}x=-x_{22}\sqrt[6]{6}$$

Combine \frac{1}{2}x and \frac{1}{2}x to get x.

$$x-\frac{11}{2}=-x_{22}\sqrt[6]{6}$$

Add \frac{11}{2} to both sides.

$$x=-x_{22}\sqrt[6]{6}+\frac{11}{2}$$

Solve for x_22

$$x_{22}=\frac{6^{\frac{5}{6}}\left(11-2x\right)}{12}$$

Steps for Solving Linear Equation

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

$$5-\frac{1}{2}x-x_{22}\sqrt[6]{6}=\frac{1}{2}x-\frac{1}{2}$$

Subtract 5 from both sides.

$$-\frac{1}{2}x-x_{22}\sqrt[6]{6}=\frac{1}{2}x-\frac{1}{2}-5$$

Subtract 5 from -\frac{1}{2} to get -\frac{11}{2}.

$$-\frac{1}{2}x-x_{22}\sqrt[6]{6}=\frac{1}{2}x-\frac{11}{2}$$

Add \frac{1}{2}x to both sides.

$$-x_{22}\sqrt[6]{6}=\frac{1}{2}x-\frac{11}{2}+\frac{1}{2}x$$

Combine \frac{1}{2}x and \frac{1}{2}x to get x.

$$-x_{22}\sqrt[6]{6}=x-\frac{11}{2}$$

The equation is in standard form.

$$\left(-\sqrt[6]{6}\right)x_{22}=x-\frac{11}{2}$$

Divide both sides by -\sqrt[6]{6}.

$$\frac{\left(-\sqrt[6]{6}\right)x_{22}}{-\sqrt[6]{6}}=\frac{x-\frac{11}{2}}{-\sqrt[6]{6}}$$

Dividing by -\sqrt[6]{6} undoes the multiplication by -\sqrt[6]{6}.

$$x_{22}=\frac{x-\frac{11}{2}}{-\sqrt[6]{6}}$$

Divide x-\frac{11}{2} by -\sqrt[6]{6}.

$$x_{22}=-\frac{2x-11}{2\sqrt[6]{6}}$$