Solve 1/sqrt{5}x-1/2(3-2x)=1

$$\frac { 1 } { \sqrt { 5 } } x - \frac { 1 } { 2 } ( 3 - 2 x ) = 1$$

Solve for x

$$x = \frac{25 - 5 \sqrt{5}}{8} \approx 1.727457514$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}x-\frac{1}{2}\left(3-2x\right)=1$$

The square of \sqrt{5} is 5.

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

Express \frac{\sqrt{5}}{5}x as a single fraction.

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

Use the distributive property to multiply -\frac{1}{2} by 3-2x.

$$\frac{\sqrt{5}x}{5}-\frac{1}{2}\times 3-\frac{1}{2}\left(-2\right)x=1$$

Express -\frac{1}{2}\times 3 as a single fraction.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Express -\frac{1}{2}\left(-2\right) as a single fraction.

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

Multiply -1 and -2 to get 2.

$$\frac{\sqrt{5}x}{5}-\frac{3}{2}+\frac{2}{2}x=1$$

Divide 2 by 2 to get 1.

$$\frac{\sqrt{5}x}{5}-\frac{3}{2}+1x=1$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{\sqrt{5}x}{5} times \frac{2}{2}. Multiply \frac{3}{2} times \frac{5}{5}.

$$\frac{2\sqrt{5}x}{10}-\frac{3\times 5}{10}+1x=1$$

Since \frac{2\sqrt{5}x}{10} and \frac{3\times 5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\sqrt{5}x-3\times 5}{10}+1x=1$$

Do the multiplications in 2\sqrt{5}x-3\times 5.

$$\frac{2\sqrt{5}x-15}{10}+1x=1$$

Multiply both sides of the equation by 10.

$$2\sqrt{5}x-15+10x=10$$

Reorder the terms.

$$2\sqrt{5}x+10x-15=10$$

Add 15 to both sides.

$$2\sqrt{5}x+10x=10+15$$

Add 10 and 15 to get 25.

$$2\sqrt{5}x+10x=25$$

Combine all terms containing x.

$$\left(2\sqrt{5}+10\right)x=25$$

Divide both sides by 2\sqrt{5}+10.

$$\frac{\left(2\sqrt{5}+10\right)x}{2\sqrt{5}+10}=\frac{25}{2\sqrt{5}+10}$$

Dividing by 2\sqrt{5}+10 undoes the multiplication by 2\sqrt{5}+10.

$$x=\frac{25}{2\sqrt{5}+10}$$

Divide 25 by 2\sqrt{5}+10.

$$x=\frac{25-5\sqrt{5}}{8}$$