Question

Carson is checking his work with Katie and finds that they disagree on a problem. Here’s what Katie wrote:

3x + 3 ≤ −2x + 5

3x ≤ −2x + 2

x ≤ 2



Is she right? Explain.

Answer 1

-3 < 2x + 5 ≤ 7

Explanation:

An inequality is a sentence with <, >, ≤, or ≥ as its verb. ... Similar statements hold for a ≤ b. ... To check, we can graph y1 = 3x - 5 and y2 = 6 - 2x. ... x ≤ 1. The solution set is x, or (-∞, 1]. The graph of the solution set is shown below. ... The sentence -3 < 2x + 5 ≤ 7 is an abbreviation for the preceding conjunction.