What is the solution set of x+2≥6 and 3x≥6

Answer 1

To find the solution set for this system of inequalities, we need to solve each inequality separately and then find the overlapping values.

First, let's solve the inequality x + 2 ≥ 6.

Subtracting 2 from both sides of the inequality, we get:
x + 2 - 2 ≥ 6 - 2
x ≥ 4

So the solution for this inequality is x ≥ 4.

Next, let's solve the inequality 3x ≥ 6.

Dividing both sides of the inequality by 3, we get:
3x/3 ≥ 6/3
x ≥ 2

So the solution for this inequality is x ≥ 2.

Now, looking at both solutions, we can see that the overlapping values are x ≥ 4 since this satisfies both inequalities.

Therefore, the solution set for the system of inequalities x + 2 ≥ 6 and 3x ≥ 6 is x ≥ 4.

Answer 2

What is the solution set of 2x−3=5 and 5x+3>−12 ?

Answer 3

To find the solution set for this system of equations, we need to solve each equation/inequality separately.

First, let's solve the equation 2x - 3 = 5.

Adding 3 to both sides of the equation, we get:
2x - 3 + 3 = 5 + 3
2x = 8

Dividing both sides of the equation by 2, we get:
2x/2 = 8/2
x = 4

So the solution for this equation is x = 4.

Next, let's solve the inequality 5x + 3 > -12.

Subtracting 3 from both sides of the inequality, we get:
5x + 3 - 3 > -12 - 3
5x > -15

Dividing both sides of the inequality by 5 (and remembering to reverse the inequality sign since we are dividing by a negative number), we get:
(5x)/5 < (-15)/5
x < -3

So the solution for this inequality is x < -3.

Now, let's look at both solutions. We see that the values that satisfy both the equation and the inequality are x = 4, since it satisfies both x = 4 (from the equation) and x < -3 (from the inequality).

Therefore, the solution set for the system of equation/inequality 2x - 3 = 5 and 5x + 3 > -12 is x = 4.