Solve x-1/2-x-2/3-x-3/4=-x-5/5

$$\frac { x - 1 } { 2 } - \frac { x - 2 } { 3 } - \frac { x - 3 } { 4 } = - \frac { x - 5 } { 5 }$$

Solve for x

$$x=\frac{5}{7}\approx 0.714285714$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 2,3,4,5.

$$30\left(x-1\right)-20\left(x-2\right)-15\left(x-3\right)=-12\left(x-5\right)$$

Use the distributive property to multiply 30 by x-1.

$$30x-30-20\left(x-2\right)-15\left(x-3\right)=-12\left(x-5\right)$$

Use the distributive property to multiply -20 by x-2.

$$30x-30-20x+40-15\left(x-3\right)=-12\left(x-5\right)$$

Combine 30x and -20x to get 10x.

$$10x-30+40-15\left(x-3\right)=-12\left(x-5\right)$$

Add -30 and 40 to get 10.

$$10x+10-15\left(x-3\right)=-12\left(x-5\right)$$

Use the distributive property to multiply -15 by x-3.

$$10x+10-15x+45=-12\left(x-5\right)$$

Combine 10x and -15x to get -5x.

$$-5x+10+45=-12\left(x-5\right)$$

Add 10 and 45 to get 55.

$$-5x+55=-12\left(x-5\right)$$

Use the distributive property to multiply -12 by x-5.

$$-5x+55=-12x+60$$

Add 12x to both sides.

$$-5x+55+12x=60$$

Combine -5x and 12x to get 7x.

$$7x+55=60$$

Subtract 55 from both sides.

$$7x=60-55$$

Subtract 55 from 60 to get 5.

$$7x=5$$

Divide both sides by 7.

$$x=\frac{5}{7}$$