What is the solution set of x+2≥6
and 3x≥6
?
To find the solution set for the inequalities x+2≥6 and 3x≥6, we'll solve each inequality separately.
First, let's solve the inequality x+2≥6:
Step 1: Subtract 2 from both sides of the inequality:
x+2-2≥6-2
x≥4
So, the solution set for x+2≥6 is x≥4.
Now, let's solve the inequality 3x≥6:
Step 1: Divide both sides of the inequality by 3:
(3x)/3≥6/3
x≥2
So, the solution set for 3x≥6 is x≥2.
The combined solution set for both inequalities is x≥4 and x≥2. However, since we are looking for the solution set where both inequalities are true, we take the intersection of the solution sets. In this case, the only value that satisfies both x≥4 and x≥2 is x≥4.
Therefore, the solution set for both inequalities is x≥4.
To find the solution set for the inequalities:
1) x + 2 ≥ 6:
Subtract 2 from both sides of the inequality,
x + 2 - 2 ≥ 6 - 2,
x ≥ 4.
The solution set for this inequality is x ≥ 4.
2) 3x ≥ 6:
Divide both sides of the inequality by 3,
(3x)/3 ≥ 6/3,
x ≥ 2.
The solution set for this inequality is x ≥ 2.
Therefore, the solution set for the pair of inequalities is x ≥ 4 and x ≥ 2. Since both inequalities have the same solution for x (x is greater than or equal to 2), the solution set is x ≥ 2.
No its not
To find the solution set for these inequalities, we need to solve each inequality separately. Let's start with the first one:
x + 2 ≥ 6
To isolate x, we need to get rid of the constant term, which is 2, on the left side of the inequality. We can do this by subtracting 2 from both sides of the inequality:
x ≥ 6 - 2
x ≥ 4
So the solution for the first inequality is x ≥ 4.
Now let's move on to the second inequality:
3x ≥ 6
To isolate x, we need to get rid of the coefficient of x, which is 3, by dividing both sides of the inequality by 3. However, we need to be careful because dividing by a negative number would change the direction of the inequality. In this case, we don't have a negative number, so we can divide by 3 without changing the direction:
(3x) / 3 ≥ 6 / 3
x ≥ 2
So the solution for the second inequality is x ≥ 2.
To find the solution set for both inequalities, we need to find the intersection of the two solution sets. In this case, we see that both inequalities have x ≥ 4 in common. So the solution set for the system of inequalities would be x ≥ 4.