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

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

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$18x-3\left(\frac{x}{2}+\frac{5}{1}\right)=60+4x$$

Anything divided by one gives itself.

$$18x-3\left(\frac{x}{2}+5\right)=60+4x$$

Subtract 4x from both sides.

$$18x-3\left(\frac{x}{2}+5\right)-4x=60$$

Multiply both sides of the equation by 2.

$$2\left(18x-3\left(\frac{x}{2}+5\right)\right)-8x=120$$

Multiply both sides of the equation by 2.

$$4\left(18x-3\left(\frac{x}{2}+5\right)\right)-16x=240$$

Use the distributive property to multiply -3 by \frac{x}{2}+5.

$$4\left(18x-3\times \frac{x}{2}-15\right)-16x=240$$

Express -3\times \frac{x}{2} as a single fraction.

$$4\left(18x+\frac{-3x}{2}-15\right)-16x=240$$

Use the distributive property to multiply 4 by 18x+\frac{-3x}{2}-15.

$$72x+4\times \frac{-3x}{2}-60-16x=240$$

Cancel out 2, the greatest common factor in 4 and 2.

$$72x+2\left(-3\right)x-60-16x=240$$

Multiply 2 and -3 to get -6.

$$72x-6x-60-16x=240$$

Combine 72x and -6x to get 66x.

$$66x-60-16x=240$$

Combine 66x and -16x to get 50x.

$$50x-60=240$$

Add 60 to both sides.

$$50x=240+60$$

Add 240 and 60 to get 300.

$$50x=300$$

Divide both sides by 50.

$$x=\frac{300}{50}$$

Divide 300 by 50 to get 6.

$$x=6$$