Solve 2(3x+1/2)-3=3+3(2x+5/3)-10

$$2 ( \frac { 3 x + 1 } { 2 } ) - 3 = 3 + 3 ( \frac { 2 x + 5 } { 3 } ) - 10$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$6\left(3x+1\right)-18=18+6\left(2x+5\right)-60$$

Use the distributive property to multiply 6 by 3x+1.

$$18x+6-18=18+6\left(2x+5\right)-60$$

Subtract 18 from 6 to get -12.

$$18x-12=18+6\left(2x+5\right)-60$$

Use the distributive property to multiply 6 by 2x+5.

$$18x-12=18+12x+30-60$$

Add 18 and 30 to get 48.

$$18x-12=48+12x-60$$

Subtract 60 from 48 to get -12.

$$18x-12=-12+12x$$

Subtract 12x from both sides.

$$18x-12-12x=-12$$

Combine 18x and -12x to get 6x.

$$6x-12=-12$$

Add 12 to both sides.

$$6x=-12+12$$

Add -12 and 12 to get 0.

$$6x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 6 is not equal to 0, x must be equal to 0.

$$x=0$$