Question

The greater of two consecutive even integers is at most fifty less than five times the smaller. Which of these represents the inequality needed to solve for the smaller integer, x, as well as its solution?

Answer 1

Inequality: 2x + 2 ≤ 5•2x - 50

Solution: x ∈ <6.5, ∞)

Explanation:

2x - the smaller of consecutive even integers

2x+2 - the greater of consecutive even integers

5•2x - five times the smaller number

5•2x-50 - fifty less than five times the smaller number

"is at most" means is less or equal

2x + 2 ≤ 5•2x - 50

2x + 2 ≤ 10x - 50

-2 -2

2x ≤ 10x - 52

-10x -10x

-8x ≤ -52

÷(-8) ÷(-8)

x ≥ 6.5

x ∈ <6.5, ∞)