Answer:
B: x > -2 and x ≤ 1
Step-by-step explanation:
–5 < 4x + 3 ≤ 7
Since -5 is less than 4x + 3, and 4x + 3 is greater than or equal to 7:
We can solve the given inequality as –5 < 4x + 3 and 4x + 3 ≤ 7 to find the possible intervals for x:
Let's start with –5 < 4x + 3 by switching or rewriting the inequality statement as:
4x + 3 > –5
Then, we can subtract 3 from both sides of the inequality to isolate 4x:
4x + 3 – 3 > –5 – 3
4x > – 8
Divide both sides of the inequality by 4:
[tex]\frac{4x}{4} > \frac{-8}{4}[/tex]
x > –2
Next, we can work on 4x + 3 ≤ 7:
4x + 3 ≤ 7
Subtract 3 from both sides of the inequality:
4x + 3 – 3 ≤ 7 – 3
4x ≤ 4
Divide both sides of the inequality by 4 to solve for x:
[tex]\frac{4x}{4} \leq \frac{4}{4}[/tex]
x ≤ 1
So, the answer is OPTION B: x > -2 and x ≤ 1
