Solve x+4/5-(x-5)=x+3/3-x-2/6

$$\frac { x + 4 } { 5 } - ( x - 5 ) = \frac { x + 3 } { 3 } - \frac { x - 2 } { 6 }$$

Solve for x

$$x = \frac{134}{29} = 4\frac{18}{29} \approx 4.620689655$$

Steps for Solving Linear Equation

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

$$6\left(x+4\right)-30\left(x-5\right)=10\left(x+3\right)-5\left(x-2\right)$$

Use the distributive property to multiply 6 by x+4.

$$6x+24-30\left(x-5\right)=10\left(x+3\right)-5\left(x-2\right)$$

Use the distributive property to multiply -30 by x-5.

$$6x+24-30x+150=10\left(x+3\right)-5\left(x-2\right)$$

Combine 6x and -30x to get -24x.

$$-24x+24+150=10\left(x+3\right)-5\left(x-2\right)$$

Add 24 and 150 to get 174.

$$-24x+174=10\left(x+3\right)-5\left(x-2\right)$$

Use the distributive property to multiply 10 by x+3.

$$-24x+174=10x+30-5\left(x-2\right)$$

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

$$-24x+174=10x+30-5x+10$$

Combine 10x and -5x to get 5x.

$$-24x+174=5x+30+10$$

Add 30 and 10 to get 40.

$$-24x+174=5x+40$$

Subtract 5x from both sides.

$$-24x+174-5x=40$$

Combine -24x and -5x to get -29x.

$$-29x+174=40$$

Subtract 174 from both sides.

$$-29x=40-174$$

Subtract 174 from 40 to get -134.

$$-29x=-134$$

Divide both sides by -29.

$$x=\frac{-134}{-29}$$

Fraction \frac{-134}{-29} can be simplified to \frac{134}{29} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{134}{29}$$