Solve 2/5(x+1)-1/2(2-3x)=1-x

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

Solve for x

$$x=\frac{16}{29}\approx 0.551724138$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{5} by x+1.

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

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

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

Cancel out 2 and 2.

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

Express -\frac{1}{2}\left(-3\right) as a single fraction.

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

Multiply -1 and -3 to get 3.

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

Convert 1 to fraction \frac{5}{5}.

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

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

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

Subtract 5 from 2 to get -3.

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

Combine \frac{2}{5}x and \frac{3}{2}x to get \frac{19}{10}x.

$$\frac{19}{10}x-\frac{3}{5}=1-x$$

Add x to both sides.

$$\frac{19}{10}x-\frac{3}{5}+x=1$$

Combine \frac{19}{10}x and x to get \frac{29}{10}x.

$$\frac{29}{10}x-\frac{3}{5}=1$$

Add \frac{3}{5} to both sides.

$$\frac{29}{10}x=1+\frac{3}{5}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{29}{10}x=\frac{5}{5}+\frac{3}{5}$$

Since \frac{5}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{29}{10}x=\frac{5+3}{5}$$

Add 5 and 3 to get 8.

$$\frac{29}{10}x=\frac{8}{5}$$

Multiply both sides by \frac{10}{29}, the reciprocal of \frac{29}{10}.

$$x=\frac{8}{5}\times \frac{10}{29}$$

Multiply \frac{8}{5} times \frac{10}{29} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{8\times 10}{5\times 29}$$

Do the multiplications in the fraction \frac{8\times 10}{5\times 29}.

$$x=\frac{80}{145}$$

Reduce the fraction \frac{80}{145} to lowest terms by extracting and canceling out 5.

$$x=\frac{16}{29}$$