Solve 10x-3/2-8x+3/9+12x+9/36=-81/4

$$\frac { 10 x - 3 } { 2 } - \frac { 8 x + 3 } { 9 } + \frac { 12 x + 9 } { 36 } = - 8 \frac { 1 } { 4 }$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 2,9,36,4.

$$18\left(10x-3\right)-4\left(8x+3\right)+12x+9=-9\left(8\times 4+1\right)$$

Use the distributive property to multiply 18 by 10x-3.

$$180x-54-4\left(8x+3\right)+12x+9=-9\left(8\times 4+1\right)$$

Use the distributive property to multiply -4 by 8x+3.

$$180x-54-32x-12+12x+9=-9\left(8\times 4+1\right)$$

Combine 180x and -32x to get 148x.

$$148x-54-12+12x+9=-9\left(8\times 4+1\right)$$

Subtract 12 from -54 to get -66.

$$148x-66+12x+9=-9\left(8\times 4+1\right)$$

Combine 148x and 12x to get 160x.

$$160x-66+9=-9\left(8\times 4+1\right)$$

Add -66 and 9 to get -57.

$$160x-57=-9\left(8\times 4+1\right)$$

Multiply 8 and 4 to get 32.

$$160x-57=-9\left(32+1\right)$$

Add 32 and 1 to get 33.

$$160x-57=-9\times 33$$

Multiply -9 and 33 to get -297.

$$160x-57=-297$$

Add 57 to both sides.

$$160x=-297+57$$

Add -297 and 57 to get -240.

$$160x=-240$$

Divide both sides by 160.

$$x=\frac{-240}{160}$$

Reduce the fraction \frac{-240}{160} to lowest terms by extracting and canceling out 80.

$$x=-\frac{3}{2}$$