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

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

Solve for x

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

Steps for Solving Linear Equation

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

$$12\left(\frac{x}{2}+\frac{1}{3}\right)=18\left(\frac{2x}{3}-\frac{1}{2}\right)+6$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{x}{2} times \frac{3}{3}. Multiply \frac{1}{3} times \frac{2}{2}.

$$12\left(\frac{3x}{6}+\frac{2}{6}\right)=18\left(\frac{2x}{3}-\frac{1}{2}\right)+6$$

Since \frac{3x}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$12\times \frac{3x+2}{6}=18\left(\frac{2x}{3}-\frac{1}{2}\right)+6$$

Cancel out 6, the greatest common factor in 12 and 6.

$$2\left(3x+2\right)=18\left(\frac{2x}{3}-\frac{1}{2}\right)+6$$

Use the distributive property to multiply 2 by 3x+2.

$$6x+4=18\left(\frac{2x}{3}-\frac{1}{2}\right)+6$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply \frac{2x}{3} times \frac{2}{2}. Multiply \frac{1}{2} times \frac{3}{3}.

$$6x+4=18\left(\frac{2\times 2x}{6}-\frac{3}{6}\right)+6$$

Since \frac{2\times 2x}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$6x+4=18\times \frac{2\times 2x-3}{6}+6$$

Do the multiplications in 2\times 2x-3.

$$6x+4=18\times \frac{4x-3}{6}+6$$

Cancel out 6, the greatest common factor in 18 and 6.

$$6x+4=3\left(4x-3\right)+6$$

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

$$6x+4=12x-9+6$$

Add -9 and 6 to get -3.

$$6x+4=12x-3$$

Subtract 12x from both sides.

$$6x+4-12x=-3$$

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

$$-6x+4=-3$$

Subtract 4 from both sides.

$$-6x=-3-4$$

Subtract 4 from -3 to get -7.

$$-6x=-7$$

Divide both sides by -6.

$$x=\frac{-7}{-6}$$

Fraction \frac{-7}{-6} can be simplified to \frac{7}{6} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{6}$$