What is the solution set of x+2≥6 and 3x≥6
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.
What is the solution set of 2x−3=5 and 5x+3>−12 ?
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.
To find the solution set for the inequality x + 2 ≥ 6, follow these steps:
Step 1: Subtract 2 from both sides of the inequality to isolate x:
x + 2 - 2 ≥ 6 - 2
x ≥ 4
Next, let's solve the second inequality, 3x ≥ 6:
Step 2: Divide both sides of the inequality by 3 to isolate x:
(3x) / 3 ≥ 6 / 3
x ≥ 2
So, the individual solution sets for each inequality are:
For x + 2 ≥ 6, the solution set is x ≥ 4.
For 3x ≥ 6, the solution set is x ≥ 2.
To find the combined solution set for both inequalities, we need to find the overlapping region between the two solution sets:
Since both inequalities have a "greater than or equal to" sign, the overlapping region is where the two inequalities are fulfilled. In this case, x is greater than or equal to the larger value between 4 and 2, which is 4.
So, the combined solution set for both inequalities is x ≥ 4.
To find the solution set for this inequality system, we need to solve each inequality separately and then find the common range of values that satisfy both inequalities.
Let's start with the first inequality: x + 2 ≥ 6.
To solve this inequality, we need to isolate x on one side of the equation.
Step 1: Subtract 2 from both sides:
x + 2 - 2 ≥ 6 - 2
x ≥ 4
So the solution to the first inequality is x ≥ 4.
Now let's move on to the second inequality: 3x ≥ 6.
Similarly, to solve this inequality, we need to isolate x on one side of the equation.
Step 1: Divide both sides by 3:
(3x)/3 ≥ 6/3
x ≥ 2
So the solution to the second inequality is x ≥ 2.
Now, let's find the common range of values that satisfy both inequalities.
Since both inequalities have the condition x ≥ (some value), we need to find the overlapping values.
The solution to the system of inequalities is x ≥ 4, as any value of x that is greater than or equal to 4 is also greater than or equal to 2.