What is the solution set of x+2≥6
and 3x≥6?(1 point)
{x|x__}
{x|x≥4}
To solve the inequality x + 2 ≥ 6, we need to isolate the variable x on one side of the inequality sign.
1. Subtract 2 from both sides of the inequality:
x + 2 - 2 ≥ 6 - 2
Simplifying, we get:
x ≥ 4
So the solution to the inequality x + 2 ≥ 6 is x ≥ 4.
To solve the inequality 3x ≥ 6, we need to isolate the variable x on one side of the inequality sign.
1. Divide both sides of the inequality by 3:
(3x)/3 ≥ 6/3
Simplifying, we get:
x ≥ 2
So the solution to the inequality 3x ≥ 6 is x ≥ 2.
Now, to find the combined solution set, we need to find the values of x that satisfy both inequalities.
Since x ≥ 4 from the first inequality, and x ≥ 2 from the second inequality, we can conclude that the solution set for both inequalities is x ≥ 4 (since any value of x that satisfies x ≥ 4 will automatically satisfy x ≥ 2 as well).
Therefore, the solution set for the given system of inequalities is {x | x ≥ 4}.