Solve 7-x-8/2=x-5/3-x-4/6

$$\frac { 7 - x - 8 } { 2 } = \frac { x - 5 } { 3 } - \frac { x - 4 } { 6 }$$

Solve for x

$$x=\frac{3}{4}=0.75$$

Steps for Solving Linear Equation

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

$$3\left(7-x-8\right)=2\left(x-5\right)-\left(x-4\right)$$

Subtract 8 from 7 to get -1.

$$3\left(-1-x\right)=2\left(x-5\right)-\left(x-4\right)$$

Use the distributive property to multiply 3 by -1-x.

$$-3-3x=2\left(x-5\right)-\left(x-4\right)$$

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

$$-3-3x=2x-10-\left(x-4\right)$$

To find the opposite of x-4, find the opposite of each term.

$$-3-3x=2x-10-x-\left(-4\right)$$

The opposite of -4 is 4.

$$-3-3x=2x-10-x+4$$

Combine 2x and -x to get x.

$$-3-3x=x-10+4$$

Add -10 and 4 to get -6.

$$-3-3x=x-6$$

Subtract x from both sides.

$$-3-3x-x=-6$$

Combine -3x and -x to get -4x.

$$-3-4x=-6$$

Add 3 to both sides.

$$-4x=-6+3$$

Add -6 and 3 to get -3.

$$-4x=-3$$

Divide both sides by -4.

$$x=\frac{-3}{-4}$$

Fraction \frac{-3}{-4} can be simplified to \frac{3}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3}{4}$$