Solve x-4/5-1/2(x+6)=x+5/3-1/2

$$\frac{ x-4 }{ 5 } - \frac{ 1 }{ 2 } (x+6)= \frac{ x+5 }{ 3 } - \frac{ 1 }{ 2 }$$

Solve for x

$$x = -\frac{149}{19} = -7\frac{16}{19} \approx -7.842105263$$

Steps for Solving Linear Equation

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

$$6\left(x-4\right)-15\left(x+6\right)=10\left(x+5\right)-15$$

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

$$6x-24-15\left(x+6\right)=10\left(x+5\right)-15$$

Use the distributive property to multiply -15 by x+6.

$$6x-24-15x-90=10\left(x+5\right)-15$$

Combine 6x and -15x to get -9x.

$$-9x-24-90=10\left(x+5\right)-15$$

Subtract 90 from -24 to get -114.

$$-9x-114=10\left(x+5\right)-15$$

Use the distributive property to multiply 10 by x+5.

$$-9x-114=10x+50-15$$

Subtract 15 from 50 to get 35.

$$-9x-114=10x+35$$

Subtract 10x from both sides.

$$-9x-114-10x=35$$

Combine -9x and -10x to get -19x.

$$-19x-114=35$$

Add 114 to both sides.

$$-19x=35+114$$

Add 35 and 114 to get 149.

$$-19x=149$$

Divide both sides by -19.

$$x=\frac{149}{-19}$$

Fraction \frac{149}{-19} can be rewritten as -\frac{149}{19} by extracting the negative sign.

$$x=-\frac{149}{19}$$