Answer: -5 < 2x - 3 < 5.
- A -5 < 2x - 3 < 5
- B 2x - 3 < 5 alone, ignoring the lower bound
- C 2x - 3 > -5 alone, ignoring the upper bound
- D 2x - 3 = 5, treating it as an equation rather than inequality
Correct answer: A. -5 < 2x - 3 < 5
Explanation: An inequality of the form |A| < k (k > 0) is equivalent to -k < A < k, here giving -5 < 2x-3 < 5, i.e. -1 < x < 4.
One-variable inequalities use open (excluded) or closed (included) circles on a number line; two-variable inequalities use a dashed (strict) or solid (non-strict) boundary line, with the solution being the entire shaded half-plane on one side of it.
Concept context
Solving linear inequalities in one and two variables algebraically and graphically, and representing solutions on a number line or as a region in a plane.