Solve 2/5-7/2x+1/2(x/1+frac{1}{3})=-frac{5}{2}+frac{x}{1}

$$\frac { 2 } { 5 } - \frac { 7 } { 2 } x + \frac { 1 } { 2 } ( \frac { x } { 1 } + \frac { 1 } { 3 } ) = - \frac { 5 } { 2 } + \frac { x } { 1 }$$

Solve for x

$$x=\frac{23}{30}\approx 0.766666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,2,3.

$$12-105x+15\left(\frac{x}{1}+\frac{1}{3}\right)=-75+30x$$

Anything divided by one gives itself.

$$12-105x+15\left(x+\frac{1}{3}\right)=-75+30x$$

Use the distributive property to multiply 15 by x+\frac{1}{3}.

$$12-105x+15x+15\times \frac{1}{3}=-75+30x$$

Multiply 15 and \frac{1}{3} to get \frac{15}{3}.

$$12-105x+15x+\frac{15}{3}=-75+30x$$

Divide 15 by 3 to get 5.

$$12-105x+15x+5=-75+30x$$

Combine -105x and 15x to get -90x.

$$12-90x+5=-75+30x$$

Add 12 and 5 to get 17.

$$17-90x=-75+30x$$

Subtract 30x from both sides.

$$17-90x-30x=-75$$

Combine -90x and -30x to get -120x.

$$17-120x=-75$$

Subtract 17 from both sides.

$$-120x=-75-17$$

Subtract 17 from -75 to get -92.

$$-120x=-92$$

Divide both sides by -120.

$$x=\frac{-92}{-120}$$

Reduce the fraction \frac{-92}{-120} to lowest terms by extracting and canceling out -4.

$$x=\frac{23}{30}$$