Solve (6/5:7/6)+2x-3/2=4/5x+12x+6*(x+1)

$$( \frac { 6 } { 5 } : \frac { 7 } { 6 } ) + 2 x - \frac { 3 } { 2 } = \frac { 4 } { 5 } x + 12 x + 6 \cdot ( x + 1 )$$

Solve for x

$$x=-\frac{151}{392}\approx -0.385204082$$

Steps for Solving Linear Equation

Divide \frac{6}{5} by \frac{7}{6} by multiplying \frac{6}{5} by the reciprocal of \frac{7}{6}.

$$\frac{6}{5}\times \frac{6}{7}+2x-\frac{3}{2}=\frac{4}{5}x+12x+6\left(x+1\right)$$

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

$$\frac{6\times 6}{5\times 7}+2x-\frac{3}{2}=\frac{4}{5}x+12x+6\left(x+1\right)$$

Do the multiplications in the fraction \frac{6\times 6}{5\times 7}.

$$\frac{36}{35}+2x-\frac{3}{2}=\frac{4}{5}x+12x+6\left(x+1\right)$$

Least common multiple of 35 and 2 is 70. Convert \frac{36}{35} and \frac{3}{2} to fractions with denominator 70.

$$\frac{72}{70}+2x-\frac{105}{70}=\frac{4}{5}x+12x+6\left(x+1\right)$$

Since \frac{72}{70} and \frac{105}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{72-105}{70}+2x=\frac{4}{5}x+12x+6\left(x+1\right)$$

Subtract 105 from 72 to get -33.

$$-\frac{33}{70}+2x=\frac{4}{5}x+12x+6\left(x+1\right)$$

Combine \frac{4}{5}x and 12x to get \frac{64}{5}x.

$$-\frac{33}{70}+2x=\frac{64}{5}x+6\left(x+1\right)$$

Use the distributive property to multiply 6 by x+1.

$$-\frac{33}{70}+2x=\frac{64}{5}x+6x+6$$

Combine \frac{64}{5}x and 6x to get \frac{94}{5}x.

$$-\frac{33}{70}+2x=\frac{94}{5}x+6$$

Subtract \frac{94}{5}x from both sides.

$$-\frac{33}{70}+2x-\frac{94}{5}x=6$$

Combine 2x and -\frac{94}{5}x to get -\frac{84}{5}x.

$$-\frac{33}{70}-\frac{84}{5}x=6$$

Add \frac{33}{70} to both sides.

$$-\frac{84}{5}x=6+\frac{33}{70}$$

Convert 6 to fraction \frac{420}{70}.

$$-\frac{84}{5}x=\frac{420}{70}+\frac{33}{70}$$

Since \frac{420}{70} and \frac{33}{70} have the same denominator, add them by adding their numerators.

$$-\frac{84}{5}x=\frac{420+33}{70}$$

Add 420 and 33 to get 453.

$$-\frac{84}{5}x=\frac{453}{70}$$

Multiply both sides by -\frac{5}{84}, the reciprocal of -\frac{84}{5}.

$$x=\frac{453}{70}\left(-\frac{5}{84}\right)$$

Multiply \frac{453}{70} times -\frac{5}{84} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{453\left(-5\right)}{70\times 84}$$

Do the multiplications in the fraction \frac{453\left(-5\right)}{70\times 84}.

$$x=\frac{-2265}{5880}$$

Reduce the fraction \frac{-2265}{5880} to lowest terms by extracting and canceling out 15.

$$x=-\frac{151}{392}$$