Solve 2(3x-4)+5(6x-7)-3x=9(x+10)+11(x+12)

$$2 ( 3 x - 4 ) + 5 ( 6 x - 7 ) - 3 x = 9 ( x + 10 ) + 11 ( x + 12 )$$

Solve for x

$$x = \frac{265}{13} = 20\frac{5}{13} \approx 20.384615385$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 3x-4.

$$6x-8+5\left(6x-7\right)-3x=9\left(x+10\right)+11\left(x+12\right)$$

Use the distributive property to multiply 5 by 6x-7.

$$6x-8+30x-35-3x=9\left(x+10\right)+11\left(x+12\right)$$

Combine 6x and 30x to get 36x.

$$36x-8-35-3x=9\left(x+10\right)+11\left(x+12\right)$$

Subtract 35 from -8 to get -43.

$$36x-43-3x=9\left(x+10\right)+11\left(x+12\right)$$

Combine 36x and -3x to get 33x.

$$33x-43=9\left(x+10\right)+11\left(x+12\right)$$

Use the distributive property to multiply 9 by x+10.

$$33x-43=9x+90+11\left(x+12\right)$$

Use the distributive property to multiply 11 by x+12.

$$33x-43=9x+90+11x+132$$

Combine 9x and 11x to get 20x.

$$33x-43=20x+90+132$$

Add 90 and 132 to get 222.

$$33x-43=20x+222$$

Subtract 20x from both sides.

$$33x-43-20x=222$$

Combine 33x and -20x to get 13x.

$$13x-43=222$$

Add 43 to both sides.

$$13x=222+43$$

Add 222 and 43 to get 265.

$$13x=265$$

Divide both sides by 13.

$$x=\frac{265}{13}$$