Solve 5x-6/4+1-2x+1/3=x

$$\frac { 5 x - 6 } { 4 } + 1 - \frac { 2 x + 1 } { 3 } = x$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{5x-6}{4} times \frac{3}{3}. Multiply \frac{2x+1}{3} times \frac{4}{4}.

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

Since \frac{3\left(5x-6\right)}{12} and \frac{4\left(2x+1\right)}{12} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\left(5x-6\right)-4\left(2x+1\right).

$$\frac{15x-18-8x-4}{12}+1=x$$

Combine like terms in 15x-18-8x-4.

$$\frac{7x-22}{12}+1=x$$

Divide each term of 7x-22 by 12 to get \frac{7}{12}x-\frac{11}{6}.

$$\frac{7}{12}x-\frac{11}{6}+1=x$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{7}{12}x-\frac{11}{6}+\frac{6}{6}=x$$

Since -\frac{11}{6} and \frac{6}{6} have the same denominator, add them by adding their numerators.

$$\frac{7}{12}x+\frac{-11+6}{6}=x$$

Add -11 and 6 to get -5.

$$\frac{7}{12}x-\frac{5}{6}=x$$

Subtract x from both sides.

$$\frac{7}{12}x-\frac{5}{6}-x=0$$

Combine \frac{7}{12}x and -x to get -\frac{5}{12}x.

$$-\frac{5}{12}x-\frac{5}{6}=0$$

Add \frac{5}{6} to both sides. Anything plus zero gives itself.

$$-\frac{5}{12}x=\frac{5}{6}$$

Multiply both sides by -\frac{12}{5}, the reciprocal of -\frac{5}{12}.

$$x=\frac{5}{6}\left(-\frac{12}{5}\right)$$

Multiply \frac{5}{6} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\left(-12\right)}{6\times 5}$$

Cancel out 5 in both numerator and denominator.

$$x=\frac{-12}{6}$$

Divide -12 by 6 to get -2.

$$x=-2$$