Solve 3/8x+2-4/5x=1+3/10x+3/2

$$\frac{ 3 }{ 8 } x+2- \frac{ 4 }{ 5 } x = 1+ \frac{ 3 }{ 10 } x+ \frac{ 3 }{ 2 }$$

Solve for x

$$x=-\frac{20}{29}\approx -0.689655172$$

Steps for Solving Linear Equation

Combine \frac{3}{8}x and -\frac{4}{5}x to get -\frac{17}{40}x.

$$-\frac{17}{40}x+2=1+\frac{3}{10}x+\frac{3}{2}$$

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

$$-\frac{17}{40}x+2=\frac{2}{2}+\frac{3}{10}x+\frac{3}{2}$$

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

$$-\frac{17}{40}x+2=\frac{2+3}{2}+\frac{3}{10}x$$

Add 2 and 3 to get 5.

$$-\frac{17}{40}x+2=\frac{5}{2}+\frac{3}{10}x$$

Subtract \frac{3}{10}x from both sides.

$$-\frac{17}{40}x+2-\frac{3}{10}x=\frac{5}{2}$$

Combine -\frac{17}{40}x and -\frac{3}{10}x to get -\frac{29}{40}x.

$$-\frac{29}{40}x+2=\frac{5}{2}$$

Subtract 2 from both sides.

$$-\frac{29}{40}x=\frac{5}{2}-2$$

Convert 2 to fraction \frac{4}{2}.

$$-\frac{29}{40}x=\frac{5}{2}-\frac{4}{2}$$

Since \frac{5}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{29}{40}x=\frac{5-4}{2}$$

Subtract 4 from 5 to get 1.

$$-\frac{29}{40}x=\frac{1}{2}$$

Multiply both sides by -\frac{40}{29}, the reciprocal of -\frac{29}{40}.

$$x=\frac{1}{2}\left(-\frac{40}{29}\right)$$

Multiply \frac{1}{2} times -\frac{40}{29} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\left(-40\right)}{2\times 29}$$

Do the multiplications in the fraction \frac{1\left(-40\right)}{2\times 29}.

$$x=\frac{-40}{58}$$

Reduce the fraction \frac{-40}{58} to lowest terms by extracting and canceling out 2.

$$x=-\frac{20}{29}$$