A) (1 point)
2t + 8 ≥ −4 (t + 1)
t ≥
-4.
To solve the inequality, we need to isolate the variable "t". Here are the steps:
1. Distribute the "-4" on the right side:
2t + 8 ≥ -4t - 4
2. Combine like terms on both sides:
2t + 4t ≥ -4 - 8
3. Simplify:
6t ≥ -12
4. Divide both sides of the inequality by 6 to solve for "t":
t ≥ -12/6
5. Simplify further:
t ≥ -2
Therefore, the solution for the inequality 2t + 8 ≥ -4 (t + 1) is t ≥ -2.
To solve the inequality, we can apply the distributive property and combine like terms. Here's how you can solve it step by step:
1. Distribute the -4 to both terms in the parentheses:
2t + 8 ≥ -4t - 4
2. Combine like terms by adding 4t to both sides of the equation:
2t + 4t + 8 ≥ -4
3. Simplify:
6t + 8 ≥ -4
4. Move the constant term (8) to the other side of the inequality by subtracting 8 from both sides:
6t ≥ -4 - 8
6t ≥ -12
5. Divide both sides of the inequality by 6 to isolate t:
(6t)/6 ≥ -12/6
t ≥ -2
Therefore, the solution to the inequality is t ≥ -2.