Solve 4(x-2)/3+3+1/8=3(6x-5)/5-9

$$\frac { 4 ( x - 2 ) } { 3 } + \frac { 3 + 1 } { 8 } = \frac { 3 ( 6 x - 5 ) } { 5 } - 9$$

Solve for x

$$x = \frac{295}{68} = 4\frac{23}{68} \approx 4.338235294$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 120, the least common multiple of 3,8,5.

$$40\times 4\left(x-2\right)+15\left(3+1\right)=24\times 3\left(6x-5\right)-1080$$

Multiply 40 and 4 to get 160.

$$160\left(x-2\right)+15\left(3+1\right)=24\times 3\left(6x-5\right)-1080$$

Use the distributive property to multiply 160 by x-2.

$$160x-320+15\left(3+1\right)=24\times 3\left(6x-5\right)-1080$$

Add 3 and 1 to get 4.

$$160x-320+15\times 4=24\times 3\left(6x-5\right)-1080$$

Multiply 15 and 4 to get 60.

$$160x-320+60=24\times 3\left(6x-5\right)-1080$$

Add -320 and 60 to get -260.

$$160x-260=24\times 3\left(6x-5\right)-1080$$

Multiply 24 and 3 to get 72.

$$160x-260=72\left(6x-5\right)-1080$$

Use the distributive property to multiply 72 by 6x-5.

$$160x-260=432x-360-1080$$

Subtract 1080 from -360 to get -1440.

$$160x-260=432x-1440$$

Subtract 432x from both sides.

$$160x-260-432x=-1440$$

Combine 160x and -432x to get -272x.

$$-272x-260=-1440$$

Add 260 to both sides.

$$-272x=-1440+260$$

Add -1440 and 260 to get -1180.

$$-272x=-1180$$

Divide both sides by -272.

$$x=\frac{-1180}{-272}$$

Reduce the fraction \frac{-1180}{-272} to lowest terms by extracting and canceling out -4.

$$x=\frac{295}{68}$$