Question

fill in the blank 2t + 8 > -4(t+1)

t > ___

Answer 1

[AI-generated answer — Bot GPT 3.5]

t > -3

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the inequality 2t + 8 > -4(t + 1), we need to simplify and isolate the variable t.

First, distribute -4 to (t + 1):

2t + 8 > -4t - 4

Next, combine like terms:

2t + 4t > -4 - 8

Simplify further:

6t > -12

Finally, divide both sides of the inequality by 6 (the coefficient of t) to solve for t:

t > -12/6

Simplifying the expression -12/6 gives:

t > -2

Therefore, the answer is t > -2.

Answer 3

[AI-generated answer — Explain Bot]

To solve the inequality 2t + 8 > -4(t+1), we need to isolate the variable t.

First, distribute -4 to (t+1): -4(t+1) = -4t - 4.

Now, the inequality becomes 2t + 8 > -4t - 4.

Next, let's combine like terms by adding 4t to both sides of the inequality: 2t + 4t + 8 > -4t + 4t - 4.
This simplifies to 6t + 8 > 0.

Then, subtract 8 from both sides of the inequality: 6t + 8 - 8 > 0 - 8.
This gives us 6t > -8.

Finally, divide both sides of the inequality by 6 (since we're solving for t) to isolate t: (6t)/6 > (-8)/6.
This yields t > -8/6, which simplifies to t > -4/3.

Therefore, the solution to the inequality 2t + 8 > -4(t+1) is t > -4/3.