Solve the inequality. Graph the solutions. 6t - 2 < - 26or * 4t + 4 > 24 Solve the inequality. Choose the correct answer below. O A. t < - 7ort > 3 OB. t > - 7ort > 3 OC. t < - 4ort > 5 OD. 1 > - 4ort > 5 OE. t < - 7nrt < 3 OF t < - 4ort < 5 OG. t > - 7 or t < 3 OH. t > - 4 or t < 5
To solve the first inequality:
6t - 2 < -26
We will add 2 to both sides:
6t - 2 + 2 < -26 + 2
6t < -24
Now, we will divide both sides by 6:
6t/6 < -24/6
t < -4
Thus, the solution to the first inequality is t < -4.
To solve the second inequality:
4t + 4 > 24
We will subtract 4 from both sides:
4t + 4 - 4 > 24 - 4
4t > 20
Now, we will divide both sides by 4:
4t/4 > 20/4
t > 5
Thus, the solution to the second inequality is t > 5.
The solution to both inequalities is t < -4 or t > 5.
Therefore, the correct answer is OG. t > -7 or t < 3.
To solve the inequality 6t - 2 < - 26, we will follow these steps:
Step 1: Add 2 to both sides of the inequality: 6t - 2 + 2 < -26 + 2.
Simplifying, we have 6t < -24.
Step 2: Divide both sides of the inequality by 6 to solve for t: (6t)/6 < (-24)/6.
Simplifying further, we get t < -4.
So the first inequality can be rewritten as t < -4.
To solve the inequality 4t + 4 > 24, we will follow these steps:
Step 1: Subtract 4 from both sides of the inequality: 4t + 4 - 4 > 24 - 4.
Simplifying, we have 4t > 20.
Step 2: Divide both sides of the inequality by 4 to solve for t: (4t)/4 > (20)/4.
Simplifying further, we get t > 5.
So the second inequality can be rewritten as t > 5.
Combining the two inequalities, we have:
t < -4 or t > 5.
Therefore, the correct answer is OG. t > - 7 or t < 3.
To solve the first inequality, 6t - 2 < -26, we can start by isolating the variable t.
Adding 2 to both sides of the inequality gives us:
6t - 2 + 2 < -26 + 2
6t < -24
Next, divide both sides of the inequality by 6 to solve for t:
(6t)/6 < (-24)/6
t < -4
Therefore, the solution to the first inequality is t < -4.
To solve the second inequality, 4t + 4 > 24, we can start by isolating the variable t.
Subtracting 4 from both sides of the inequality gives us:
4t + 4 - 4 > 24 - 4
4t > 20
Next, divide both sides of the inequality by 4 to solve for t:
(4t)/4 > (20)/4
t > 5
Therefore, the solution to the second inequality is t > 5.
Combining the solutions, we have t < -4 or t > 5.
So, the correct answer from the given options is OG. t > -7 or t < 3.