Question

Use the inequality 3x – 5 < 8 to answer #1 and #2. 1. Represent the solution set to 3x - 5 < 8 on the number line below. + 8 -10 -8 -6 -4 -2 0 N 4 6 10 3 2 2. Which of the following is NOT in the solution set of 3x – 4 < 8? Select all that apply. (A) A (B) 4 (C) 4.5 (D) 2 - 121 13 VIEW

Answer 1

consider the inequality

$3x-5<\text{ 8}$

this is equivalent to:

$3x<\text{ 8 + 5}$

this is equivalent to

$3x<\text{ 8 + 5 = 13}$

this is equivalent to say:

$3x<\text{ 13}$

solve for x:

$x<\text{ }\frac{13}{3}=4.3$

so, the correct answer for the second problem is (C) 4.5 , because 4.5 > 4.3 so 4.5 is not in the interval ( -infinity,4.3)

For problem 1, note that we have the following interval

$(-\infty,4.3)$

on the Real line that is: