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

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

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,3,2,6.

$$6\left(x+2\right)-10\left(1-\frac{2x-5}{2}\right)=5\left(2x-5\right)$$

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

$$6x+12-10\left(1-\frac{2x-5}{2}\right)=5\left(2x-5\right)$$

Use the distributive property to multiply 5 by 2x-5.

$$6x+12-10\left(1-\frac{2x-5}{2}\right)=10x-25$$

Divide each term of 2x-5 by 2 to get x-\frac{5}{2}.

$$6x+12-10\left(1-\left(x-\frac{5}{2}\right)\right)=10x-25$$

To find the opposite of x-\frac{5}{2}, find the opposite of each term.

$$6x+12-10\left(1-x-\left(-\frac{5}{2}\right)\right)=10x-25$$

The opposite of -\frac{5}{2} is \frac{5}{2}.

$$6x+12-10\left(1-x+\frac{5}{2}\right)=10x-25$$

Convert 1 to fraction \frac{2}{2}.

$$6x+12-10\left(\frac{2}{2}-x+\frac{5}{2}\right)=10x-25$$

Since \frac{2}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$6x+12-10\left(\frac{2+5}{2}-x\right)=10x-25$$

Add 2 and 5 to get 7.

$$6x+12-10\left(\frac{7}{2}-x\right)=10x-25$$

Use the distributive property to multiply -10 by \frac{7}{2}-x.

$$6x+12-10\times \frac{7}{2}+10x=10x-25$$

Express -10\times \frac{7}{2} as a single fraction.

$$6x+12+\frac{-10\times 7}{2}+10x=10x-25$$

Multiply -10 and 7 to get -70.

$$6x+12+\frac{-70}{2}+10x=10x-25$$

Divide -70 by 2 to get -35.

$$6x+12-35+10x=10x-25$$

Subtract 35 from 12 to get -23.

$$6x-23+10x=10x-25$$

Combine 6x and 10x to get 16x.

$$16x-23=10x-25$$

Subtract 10x from both sides.

$$16x-23-10x=-25$$

Combine 16x and -10x to get 6x.

$$6x-23=-25$$

Add 23 to both sides.

$$6x=-25+23$$

Add -25 and 23 to get -2.

$$6x=-2$$

Divide both sides by 6.

$$x=\frac{-2}{6}$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{3}$$