Solve -9x-6/4--x+1/2=x-9/6

$$\frac { - 9 x - 6 } { 4 } - \frac { - x + 1 } { 2 } = \frac { x - 9 } { 6 }$$

Solve for x

$$x=-\frac{6}{23}\approx -0.260869565$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 4,2,6.

$$3\left(-9x-6\right)-6\left(-x+1\right)=2\left(x-9\right)$$

Use the distributive property to multiply 3 by -9x-6.

$$-27x-18-6\left(-x+1\right)=2\left(x-9\right)$$

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

$$-27x-18-6\left(-x\right)-6=2\left(x-9\right)$$

Multiply -6 and -1 to get 6.

$$-27x-18+6x-6=2\left(x-9\right)$$

Combine -27x and 6x to get -21x.

$$-21x-18-6=2\left(x-9\right)$$

Subtract 6 from -18 to get -24.

$$-21x-24=2\left(x-9\right)$$

Use the distributive property to multiply 2 by x-9.

$$-21x-24=2x-18$$

Subtract 2x from both sides.

$$-21x-24-2x=-18$$

Combine -21x and -2x to get -23x.

$$-23x-24=-18$$

Add 24 to both sides.

$$-23x=-18+24$$

Add -18 and 24 to get 6.

$$-23x=6$$

Divide both sides by -23.

$$x=\frac{6}{-23}$$

Fraction \frac{6}{-23} can be rewritten as -\frac{6}{23} by extracting the negative sign.

$$x=-\frac{6}{23}$$