Solve -left(-3x-3right)/-2left(-5x-3right)/4+5/5=1+12x-3/3-frac{9}{1}

$$\frac{ - \left( -3x-3 \right) }{ } - \frac{ 2 \left( -5x-3 \right) }{ 4 } + \frac{ 5 }{ 5 } = 1+ \frac{ 12x-3 }{ 3 } - \frac{ 9 }{ 1 }$$

Solve for x

$$x = -\frac{29}{3} = -9\frac{2}{3} \approx -9.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 4,5,3.

$$60\left(-\left(-3x-3\right)\right)-15\times 2\left(-5x-3\right)+12\times 5=60+20\left(12x-3\right)-60\times 9$$

To find the opposite of -3x-3, find the opposite of each term.

$$60\left(-\left(-3x\right)-\left(-3\right)\right)-15\times 2\left(-5x-3\right)+12\times 5=60+20\left(12x-3\right)-60\times 9$$

The opposite of -3x is 3x.

$$60\left(3x-\left(-3\right)\right)-15\times 2\left(-5x-3\right)+12\times 5=60+20\left(12x-3\right)-60\times 9$$

The opposite of -3 is 3.

$$60\left(3x+3\right)-15\times 2\left(-5x-3\right)+12\times 5=60+20\left(12x-3\right)-60\times 9$$

Use the distributive property to multiply 60 by 3x+3.

$$180x+180-15\times 2\left(-5x-3\right)+12\times 5=60+20\left(12x-3\right)-60\times 9$$

Multiply -15 and 2 to get -30.

$$180x+180-30\left(-5x-3\right)+12\times 5=60+20\left(12x-3\right)-60\times 9$$

Use the distributive property to multiply -30 by -5x-3.

$$180x+180+150x+90+12\times 5=60+20\left(12x-3\right)-60\times 9$$

Combine 180x and 150x to get 330x.

$$330x+180+90+12\times 5=60+20\left(12x-3\right)-60\times 9$$

Add 180 and 90 to get 270.

$$330x+270+12\times 5=60+20\left(12x-3\right)-60\times 9$$

Multiply 12 and 5 to get 60.

$$330x+270+60=60+20\left(12x-3\right)-60\times 9$$

Add 270 and 60 to get 330.

$$330x+330=60+20\left(12x-3\right)-60\times 9$$

Use the distributive property to multiply 20 by 12x-3.

$$330x+330=60+240x-60-60\times 9$$

Subtract 60 from 60 to get 0.

$$330x+330=240x-60\times 9$$

Multiply -60 and 9 to get -540.

$$330x+330=240x-540$$

Subtract 240x from both sides.

$$330x+330-240x=-540$$

Combine 330x and -240x to get 90x.

$$90x+330=-540$$

Subtract 330 from both sides.

$$90x=-540-330$$

Subtract 330 from -540 to get -870.

$$90x=-870$$

Divide both sides by 90.

$$x=\frac{-870}{90}$$

Reduce the fraction \frac{-870}{90} to lowest terms by extracting and canceling out 30.

$$x=-\frac{29}{3}$$