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

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,6.

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

Multiply 6 and 3 to get 18.

$$18\left(x+1\right)=5\left(-2\left(3x-4\right)+2\right)$$

Use the distributive property to multiply 18 by x+1.

$$18x+18=5\left(-2\left(3x-4\right)+2\right)$$

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

$$18x+18=5\left(-6x+8+2\right)$$

Add 8 and 2 to get 10.

$$18x+18=5\left(-6x+10\right)$$

Use the distributive property to multiply 5 by -6x+10.

$$18x+18=-30x+50$$

Add 30x to both sides.

$$18x+18+30x=50$$

Combine 18x and 30x to get 48x.

$$48x+18=50$$

Subtract 18 from both sides.

$$48x=50-18$$

Subtract 18 from 50 to get 32.

$$48x=32$$

Divide both sides by 48.

$$x=\frac{32}{48}$$

Reduce the fraction \frac{32}{48} to lowest terms by extracting and canceling out 16.

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