Tricky Absolute Value! #2

Since $x+1, x+2, x+3$ and $x+4$ are consecutive numbers, $|x+1|+|x+2|+|x+3|+|x+4|$ must be larger than 0.

Therefore, $10x$ must be larger than 0. Since 10 is larger than 0, $x$ must be larger than 0.

Therefore, $x+1, x+2, x+3$ and $x+4$ are positive numbers.

Hence, we can rewrite the expression as $x+1+x+2+x+3+x+4=10x$

Solving this equation gives us the answer: $x=\frac{5}{3}$ . Therefore the required answer is $5+3=\boxed{8}$

combining the terms we get that 4x+10=10x. From here we can see that 10=10x-4x=6x. so x=10÷6. 10 and 6 can be reduced by two to be 3 and 5. 3 and 5 are both primes so cant be reduced further and the answer is then going to be 3+5=8.