Solve 3/2-2-6x=-3x+12/13

$$\frac { 3 } { 2 } - 2 - 6 x = - 3 x + \frac { 12 } { 13 }$$

Solve for x

$$x=-\frac{37}{78}\approx -0.474358974$$

Steps for Solving Linear Equation

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

$$\frac{3}{2}-\frac{4}{2}-6x=-3x+\frac{12}{13}$$

Since \frac{3}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-4}{2}-6x=-3x+\frac{12}{13}$$

Subtract 4 from 3 to get -1.

$$-\frac{1}{2}-6x=-3x+\frac{12}{13}$$

Add 3x to both sides.

$$-\frac{1}{2}-6x+3x=\frac{12}{13}$$

Combine -6x and 3x to get -3x.

$$-\frac{1}{2}-3x=\frac{12}{13}$$

Add \frac{1}{2} to both sides.

$$-3x=\frac{12}{13}+\frac{1}{2}$$

Least common multiple of 13 and 2 is 26. Convert \frac{12}{13} and \frac{1}{2} to fractions with denominator 26.

$$-3x=\frac{24}{26}+\frac{13}{26}$$

Since \frac{24}{26} and \frac{13}{26} have the same denominator, add them by adding their numerators.

$$-3x=\frac{24+13}{26}$$

Add 24 and 13 to get 37.

$$-3x=\frac{37}{26}$$

Divide both sides by -3.

$$x=\frac{\frac{37}{26}}{-3}$$

Express \frac{\frac{37}{26}}{-3} as a single fraction.

$$x=\frac{37}{26\left(-3\right)}$$

Multiply 26 and -3 to get -78.

$$x=\frac{37}{-78}$$

Fraction \frac{37}{-78} can be rewritten as -\frac{37}{78} by extracting the negative sign.

$$x=-\frac{37}{78}$$