Solve 1/5x-1/2left(3-2xright)=1

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

Solve for x

$$x = \frac{25}{12} = 2\frac{1}{12} \approx 2.083333333$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

Multiply -1 and -2 to get 2.

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

Divide 2 by 2 to get 1.

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

Combine \frac{1}{5}x and 1x to get \frac{6}{5}x.

$$\frac{6}{5}x-\frac{3}{2}=1$$

Add \frac{3}{2} to both sides.

$$\frac{6}{5}x=1+\frac{3}{2}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{6}{5}x=\frac{2}{2}+\frac{3}{2}$$

Since \frac{2}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{6}{5}x=\frac{2+3}{2}$$

Add 2 and 3 to get 5.

$$\frac{6}{5}x=\frac{5}{2}$$

Multiply both sides by \frac{5}{6}, the reciprocal of \frac{6}{5}.

$$x=\frac{5}{2}\times \frac{5}{6}$$

Multiply \frac{5}{2} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 5}{2\times 6}$$

Do the multiplications in the fraction \frac{5\times 5}{2\times 6}.

$$x=\frac{25}{12}$$