2t + 8 ≥ −4(t + 1)t ≥ _____(1 point)Responsesnegative seven sixthsImage with alt text: negative seven sixths–2–2–6–62
To solve the inequality 2t + 8 ≥ −4(t + 1), we need to simplify and isolate the variable t.
First, distribute the -4 to the terms inside the parentheses:
2t + 8 ≥ -4t - 4
Next, combine like terms:
2t + 4t ≥ -8 - 4
Simplifying further:
6t ≥ -12
Now, divide both sides by 6, remembering to reverse the inequality sign since we are dividing by a negative number:
t ≤ -12/6
Simplifying the inequality:
t ≤ -2
So, the answer is t ≤ -2.
Therefore, the missing number in the inequality t ≥ _____ is -2.