Solve the compound inequality:
2t≤-4 or 7t≥49
To solve the compound inequality, we need to solve each inequality separately and then combine the solutions.
First, let's solve the inequality 2t ≤ -4:
Divide both sides of the inequality by 2 to isolate t:
t ≤ -4/2
t ≤ -2
Now, let's solve the inequality 7t ≥ 49:
Divide both sides of the inequality by 7 to isolate t:
t ≥ 49/7
t ≥ 7
Now, let's combine the solutions:
-2 ≤ t ≤ 7
Therefore, the solution to the compound inequality 2t≤-4 or 7t≥49 is -2 ≤ t ≤ 7.
To solve the compound inequality, we will start by solving each inequality separately and then combining the solutions.
Let's solve the first inequality:
2t ≤ -4
To isolate t, we need to divide both sides of the inequality by 2. However, when we divide by a negative number, the inequality sign flips. Since dividing by 2 doesn't change the inequality sign, we don't need to flip it:
2t/2 ≤ -4/2
t ≤ -2
Now let's solve the second inequality:
7t ≥ 49
To isolate t, we need to divide both sides of the inequality by 7. However, when we divide by a negative number, the inequality sign flips. Since dividing by 7 doesn't change the inequality sign, we don't need to flip it:
7t/7 ≥ 49/7
t ≥ 7
Now we combine the solutions by taking the intersection of the two solution sets:
t ≤ -2 or t ≥ 7
So, the solution to the compound inequality is t ≤ -2 or t ≥ 7.
To solve the compound inequality, we will solve each inequality separately and then combine the solution sets.
Solving the first inequality, 2t ≤ -4:
Divide both sides of the inequality by 2 (since the coefficient of t is 2 and we want to isolate t):
t ≤ -4/2
t ≤ -2
Solving the second inequality, 7t ≥ 49:
Divide both sides of the inequality by 7 (since the coefficient of t is 7 and we want to isolate t):
t ≥ 49/7
t ≥ 7
Combining the two solutions, we have t ≤ -2 or t ≥ 7.