Answer:
C: -4.13
Step-by-step explanation:
To find out which value of [tex]\sf x[/tex] makes the inequality [tex]\sf 2.6 + 2x > -5.9[/tex] true, we can solve the inequality step by step.
Given inequality:
[tex]\sf 2.6 + 2x > -5.9 [/tex]
Subtract [tex]\sf 2.6[/tex] from both sides:
[tex]\sf 2x > -5.9 - 2.6 [/tex]
[tex]\sf 2x > -8.5 [/tex]
Now, divide both sides by [tex]\sf 2[/tex] to isolate [tex]\sf x[/tex]:
[tex]\sf x > \dfrac{-8.5}{2} [/tex]
[tex]\sf x > -4.25 [/tex]
We are looking for the value of [tex]\sf x[/tex] that is greater than [tex]\sf -4.25[/tex].
Let's compare the answer choices with [tex]\sf -4.25[/tex] to determine which value of [tex]\sf x[/tex] satisfies the inequality.
A: [tex]\sf -4.47[/tex]
[tex]\sf -4.47 > -4.25 [/tex] (False)
B: [tex]\sf -4.37[/tex]
[tex]\sf -4.37 > -4.25 [/tex] (False)
C: [tex]\sf -4.13[/tex]
[tex]\sf -4.13 > -4.25 [/tex] (True)
D: [tex]\sf -4.43[/tex]
[tex]\sf -4.43 > -4.25 [/tex] (False)
Therefore, the correct answer choice is:
C: -4.13