Solve the inequality. Graph the solutions.

Question

|x + 20/5| >4
O A. The solution is x<
or X>
• B. The solution is x=
• C. The solution is
<X<
• D. The solution is all real numbers.
• E. There is no solution.
• (Type integers or simplified fractions.)
• (Type an integer or a simplified fraction.)
• (Type integers or simplified fractions.)

Answer 1

To solve the inequality |x + 20/5| > 4, we can break it down into two separate inequalities:

1) x + 20/5 > 4
2) x + 20/5 < -4

Solving the first inequality:
x + 20/5 > 4
x + 4 > 4
x > 4 - 4
x > 0

Solving the second inequality:
x + 20/5 < -4
x + 4 < -4
x < -4 - 4
x < -8

Combining the two solutions, we have x > 0 or x < -8.

Graphically, this can be represented as an open circle at x = 0 and an open circle at x = -8, with a shaded region in between.