Solve 2+(x+2)/2+(x+2)/5=1/10

$$\frac { 2 + ( x + 2 ) } { 2 } + \frac { ( x + 2 ) } { 5 } = \frac { 1 } { 10 }$$

Solve for x

$$x = -\frac{23}{7} = -3\frac{2}{7} \approx -3.285714286$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 2,5,10.

$$5\left(2+x+2\right)+2\left(x+2\right)=1$$

Add 2 and 2 to get 4.

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

Use the distributive property to multiply 5 by 4+x.

$$20+5x+2\left(x+2\right)=1$$

Use the distributive property to multiply 2 by x+2.

$$20+5x+2x+4=1$$

Combine 5x and 2x to get 7x.

$$20+7x+4=1$$

Add 20 and 4 to get 24.

$$24+7x=1$$

Subtract 24 from both sides.

$$7x=1-24$$

Subtract 24 from 1 to get -23.

$$7x=-23$$

Divide both sides by 7.

$$x=\frac{-23}{7}$$

Fraction \frac{-23}{7} can be rewritten as -\frac{23}{7} by extracting the negative sign.

$$x=-\frac{23}{7}$$