What is the solution set of x+2≥6 and 3x≥6?
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The solution set is:
{x ≥ 4/3}
To find the solution set of the inequalities x + 2 ≥ 6 and 3x ≥ 6, we will solve each inequality separately and then combine the solution sets.
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}
To find the solution set of the system of inequalities, we will solve each inequality separately and then determine the values of 'x' that satisfy both inequalities.
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}.