The solution set is:
{x ≥ 4/3}
{ }
{x ≥ 4/3}
Step 1: Solve the inequality x + 2 ≥ 6.
Subtracting 2 from both sides, we get:
x ≥ 4
Step 2: Solve the inequality 3x ≥ 6.
Dividing both sides by 3, we get:
x ≥ 2
Step 3: Combine the solution sets.
Since x ≥ 4 and x ≥ 2, the solution set is the intersection of these two sets. In other words, x must satisfy both conditions. Therefore, the solution set is:
{x | x ≥ 4}
First, let's solve the inequality x + 2 ≥ 6.
1. Subtract 2 from both sides: x ≥ 4.
Now, let's solve the inequality 3x ≥ 6.
2. Divide both sides by 3: x ≥ 2.
Since both inequalities have the same variable 'x' and both have the "greater than or equal to" symbol, we need to find the values of 'x' that satisfy both of them.
3. The values of 'x' that satisfy both inequalities are the ones greater than or equal to the larger value obtained from the individual inequalities, which in this case is 4.
Therefore, the solution set is {x | x ≥ 4}.