use this inequality -4t - 8 less than or equal to 12 to fill in the missing number, t+4 greater than or equal to ___?
-4t-8 ≤ 12
Add 8 to both sides.
-4t ≤ 20
Divide both sides by -4, which changes the direction of the carat.
t ≥ -5
Can you do the rest?
To solve this problem, we will start by rearranging the given inequality:
-4t - 8 ≤ 12
To solve for t, we need to isolate the variable on one side of the inequality. First, let's get rid of the -8 by adding 8 to both sides:
-4t ≤ 12 + 8
Simplifying:
-4t ≤ 20
Next, we want to get rid of the coefficient -4 in front of the t. Since it is a negative number, we can multiply both sides of the inequality by -1 to eliminate it while also flipping the direction of the inequality sign. However, when we multiply or divide an inequality by a negative number, we need to reverse the inequality sign. Hence, we have:
-1(-4t) ≥ -1(20)
4t ≥ -20
Now, to solve for t, we can divide both sides by 4:
(4t)/4 ≥ (-20)/4
t ≥ -5
So, the solution to the inequality -4t - 8 ≤ 12 is t ≥ -5.
To find the missing number in the inequality t + 4 ≥ ___, we notice that the inequality t ≥ -5 means that t is greater than or equal to -5. So, for the inequality t + 4 ≥ ___, if t is greater than or equal to -5, then t + 4 will be greater than or equal to -5 + 4.
Therefore, the missing number is -1.
Hence, t + 4 ≥ -1 is the completed inequality.