Solve 4x-52+25/12=32x-9/6

$$4x-52+ \frac{ 25 }{ 12 } =32x- \frac{ 9 }{ 6 }$$

Solve for x

$$x = -\frac{83}{48} = -1\frac{35}{48} \approx -1.729166667$$

Steps for Solving Linear Equation

Convert -52 to fraction -\frac{624}{12}.

$$4x-\frac{624}{12}+\frac{25}{12}=32x-\frac{9}{6}$$

Since -\frac{624}{12} and \frac{25}{12} have the same denominator, add them by adding their numerators.

$$4x+\frac{-624+25}{12}=32x-\frac{9}{6}$$

Add -624 and 25 to get -599.

$$4x-\frac{599}{12}=32x-\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$4x-\frac{599}{12}=32x-\frac{3}{2}$$

Subtract 32x from both sides.

$$4x-\frac{599}{12}-32x=-\frac{3}{2}$$

Combine 4x and -32x to get -28x.

$$-28x-\frac{599}{12}=-\frac{3}{2}$$

Add \frac{599}{12} to both sides.

$$-28x=-\frac{3}{2}+\frac{599}{12}$$

Least common multiple of 2 and 12 is 12. Convert -\frac{3}{2} and \frac{599}{12} to fractions with denominator 12.

$$-28x=-\frac{18}{12}+\frac{599}{12}$$

Since -\frac{18}{12} and \frac{599}{12} have the same denominator, add them by adding their numerators.

$$-28x=\frac{-18+599}{12}$$

Add -18 and 599 to get 581.

$$-28x=\frac{581}{12}$$

Divide both sides by -28.

$$x=\frac{\frac{581}{12}}{-28}$$

Express \frac{\frac{581}{12}}{-28} as a single fraction.

$$x=\frac{581}{12\left(-28\right)}$$

Multiply 12 and -28 to get -336.

$$x=\frac{581}{-336}$$

Reduce the fraction \frac{581}{-336} to lowest terms by extracting and canceling out 7.

$$x=-\frac{83}{48}$$