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

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

Solve for x

$$x = -\frac{25}{6} = -4\frac{1}{6} \approx -4.166666667$$

Steps for Solving Linear Equation

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

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

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

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

Multiply -2 and 2 to get -4.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

Combine \frac{3}{5}x and -2x to get -\frac{7}{5}x.

$$\frac{1}{2}-\frac{7}{5}x-\frac{4}{3}=5$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{3}{6}-\frac{7}{5}x-\frac{8}{6}=5$$

Since \frac{3}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-8}{6}-\frac{7}{5}x=5$$

Subtract 8 from 3 to get -5.

$$-\frac{5}{6}-\frac{7}{5}x=5$$

Add \frac{5}{6} to both sides.

$$-\frac{7}{5}x=5+\frac{5}{6}$$

Convert 5 to fraction \frac{30}{6}.

$$-\frac{7}{5}x=\frac{30}{6}+\frac{5}{6}$$

Since \frac{30}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$-\frac{7}{5}x=\frac{30+5}{6}$$

Add 30 and 5 to get 35.

$$-\frac{7}{5}x=\frac{35}{6}$$

Multiply both sides by -\frac{5}{7}, the reciprocal of -\frac{7}{5}.

$$x=\frac{35}{6}\left(-\frac{5}{7}\right)$$

Multiply \frac{35}{6} times -\frac{5}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{35\left(-5\right)}{6\times 7}$$

Do the multiplications in the fraction \frac{35\left(-5\right)}{6\times 7}.

$$x=\frac{-175}{42}$$

Reduce the fraction \frac{-175}{42} to lowest terms by extracting and canceling out 7.

$$x=-\frac{25}{6}$$