use the inequality -4t-8 is less than or equal to 12
a. t is greater than or equal to ?
b. t + 4 is greater than or equal to ?
c. t- ? is greater than or equal to 0
d. t + 10 is greater than or equal to ?
e. 3t is greater than or equal to ?
f. t/? is greater than or equal to -5
if x is not equal to 0 then u/x + 5u/x - u/5x =
To solve the inequality -4t-8 ≤ 12, we will go through each step.
Step 1: Add 8 to both sides of the inequality to isolate the term "-4t":
-4t ≤ 20
Step 2: Divide both sides of the inequality by -4:
t ≥ -5
So, the solutions are:
a. t is greater than or equal to -5.
b. t + 4 is greater than or equal to -1.
c. t - (-5) is greater than or equal to 0. Simplifying, we get t + 5 ≥ 0.
d. t + 10 is greater than or equal to 5.
e. 3t is greater than or equal to -15.
f. t/(-5) is greater than or equal to -5.
To solve the inequality -4t - 8 ≤ 12, we need to isolate the variable t.
Step 1: Add 8 to both sides of the inequality:
-4t - 8 + 8 ≤ 12 + 8
-4t ≤ 20
Step 2: Divide both sides of the inequality by -4. Since we are dividing by a negative number, the inequality sign flips:
t ≥ 20 / -4
t ≥ -5
a. t is greater than or equal to -5.
To solve the other parts:
b. Adding 4 to both sides of the initial inequality:
-4t - 8 + 4 ≤ 12 + 4
-4t - 4 ≤ 16
-4t ≤ 20
t ≥ 20 / -4
t ≥ -5
t + 4 is greater than or equal to -1.
c. Subtracting a variable t from both sides of the initial inequality:
-4t - t - 8 ≤ 12 - t
-5t - 8 ≤ 12 - t
-5t ≤ 20 - t
-4t ≤ 20
t ≥ 20 / -4
t ≥ -5
t - (-5) is greater than or equal to 0.
d. Adding 10 to both sides of the initial inequality:
-4t - 8 + 10 ≤ 12 + 10
-4t + 2 ≤ 22
-4t ≤ 20
t ≥ 20 / -4
t ≥ -5
t + 10 is greater than or equal to 5.
e. Multiplying both sides of the initial inequality by 3 (since we need to isolate t):
-4t - 8 ≤ 12
-12t - 24 ≤ 36
-12t ≤ 60
t ≥ 60 / -12
t ≥ -5
3t is greater than or equal to -15.
f. Dividing both sides of the initial inequality by the variable t:
-4t - 8 ≤ 12
-8/(-4t) - (8/t) ≤ 12 / t
2 + (8/t) ≤ 12 / t
2t/t + 8/t ≤ 12/t
(2t + 8) / t ≤ 12/t
Since the inequality involves dividing by t, we need to check if t can be equal to 0. If not, we can multiply both sides of the inequality by t to eliminate the denominator:
If t ≠ 0:
2t + 8 ≤ 12
2t ≤ 4
t ≤ 4 / 2
t ≤ 2
t/? is greater than or equal to -5 when t is greater than or equal to 2.