Math problem: If Alexander the Great had lived 9 years more his reign would have lasted 1/2 his life, while if he had lived 9 years less his reign would have lasted 1/8 of his life. How old was Alexander when he died? And how long did he reign?

lived 48 years

              reigned for 15 years

Step-by-step explanation:

Let x represent the number of years he reigned.

Let y represent Alexander's age.

Use the given information to create a system of equations:

Equation 1:      x + 9 = (1/2)y

Equation 2:     x - 9 = (1/8)y

Multiply the second equation by -1 and add the equations to eliminate x:

Input y = 48 into either equation to solve for x:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5