Solve 11*(12-x)-30=20x+59-6*(4x-13)quad[-5]

$$11 \cdot ( 12 - x ) - 30 = 20 x + 59 - 6 \cdot ( 4 x - 13 ) \quad [ - 5 ]$$

Solve for x

$$x = \frac{433}{151} = 2\frac{131}{151} \approx 2.867549669$$

Steps for Solving Linear Equation

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

$$132-11x-30=20x+59-6\left(4x-13\right)\left(-5\right)$$

Subtract 30 from 132 to get 102.

$$102-11x=20x+59-6\left(4x-13\right)\left(-5\right)$$

Multiply 6 and -5 to get -30.

$$102-11x=20x+59-\left(-30\left(4x-13\right)\right)$$

The opposite of -30\left(4x-13\right) is 30\left(4x-13\right).

$$102-11x=20x+59+30\left(4x-13\right)$$

Use the distributive property to multiply 30 by 4x-13.

$$102-11x=20x+59+120x-390$$

Combine 20x and 120x to get 140x.

$$102-11x=140x+59-390$$

Subtract 390 from 59 to get -331.

$$102-11x=140x-331$$

Subtract 140x from both sides.

$$102-11x-140x=-331$$

Combine -11x and -140x to get -151x.

$$102-151x=-331$$

Subtract 102 from both sides.

$$-151x=-331-102$$

Subtract 102 from -331 to get -433.

$$-151x=-433$$

Divide both sides by -151.

$$x=\frac{-433}{-151}$$

Fraction \frac{-433}{-151} can be simplified to \frac{433}{151} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{433}{151}$$