Question

For what values of n is the difference (2 - 2n) - (5n - 27) positive?

a) n < 4
b) n > 4
c) n = 4
d) No solution

Answer 1

To determine the values of n for which the difference (2 - 2n) - (5n - 27) is positive, simplify the expression, set it greater than zero, and solve the inequality. The values of n for which the difference is positive are n < 4.

Step-by-step explanation:

To determine the values of n for which the difference (2 - 2n) - (5n - 27) is positive, we need to simplify the expression and set it greater than zero. First, distribute the negative sign in the second term:

2 - 2n - 5n + 27 > 0

Combine like terms:

-7n + 29 > 0

Now, solve the inequality by isolating n. Subtract 29 from both sides:

-7n > -29

Divide both sides by -7, remembering to reverse the inequality sign because we're dividing by a negative number:

n < 4

Therefore, the values of n for which the difference is positive are n < 4.