Solve x+5/8=1/4+x-7/5

$$\frac { x + 5 } { 8 } = \frac { 1 } { 4 } + \frac { x - 7 } { 5 }$$

Solve for x

$$x = \frac{71}{3} = 23\frac{2}{3} \approx 23.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 8,4,5.

$$5\left(x+5\right)=10+8\left(x-7\right)$$

Use the distributive property to multiply 5 by x+5.

$$5x+25=10+8\left(x-7\right)$$

Use the distributive property to multiply 8 by x-7.

$$5x+25=10+8x-56$$

Subtract 56 from 10 to get -46.

$$5x+25=-46+8x$$

Subtract 8x from both sides.

$$5x+25-8x=-46$$

Combine 5x and -8x to get -3x.

$$-3x+25=-46$$

Subtract 25 from both sides.

$$-3x=-46-25$$

Subtract 25 from -46 to get -71.

$$-3x=-71$$

Divide both sides by -3.

$$x=\frac{-71}{-3}$$

Fraction \frac{-71}{-3} can be simplified to \frac{71}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{71}{3}$$