Solve the inequality. Graph the solution set and write it in interval notation.
2/5 * x > 5
Write the answer in interval notation.
___
To solve the inequality, we need to isolate the variable x.
First, we can begin by multiplying both sides of the inequality by 5/2 (the reciprocal of 2/5) to get rid of the fraction:
(2/5) * (5/2) * x > 5 * (5/2)
This simplifies to:
x > 25/2
To graph the solution set, we start by drawing a number line and marking a closed circle at 25/2 (since the inequality is greater than and not equal to). Then, we draw an arrow to the right to represent all values greater than 25/2. The graph would look like this:
------------------------------------------------->
| o
25/2
In interval notation, the solution set would be (25/2, ∞).
To solve the inequality 2/5 * x > 5, we can begin by multiplying both sides of the inequality by 5 to eliminate the fraction. However, since 5 is positive, we don't need to change the direction of the inequality.
2/5 * x > 5
Multiplying both sides by 5:
(2/5) * 5 * x > 5 * 5
2x > 25
Now, to isolate x, we divide both sides of the inequality by 2:
(2x)/2 > 25/2
x > 25/2
The solution to the inequality is x > 25/2.
Now let's graph the solution set on a number line:
--------------(25/2)-------------->
(-∞) (25/2) (+∞)
The solution set is all values of x greater than (but not equal to) 25/2. In interval notation, this can be written as:
(25/2, +∞)
To solve the inequality 2/5 * x > 5, we can follow these steps:
1. Start by multiplying both sides of the inequality by the reciprocal of 2/5, which is 5/2. This step is necessary because multiplying or dividing both sides of an inequality by a negative number requires reversing the direction of the inequality symbol.
(2/5 * x) * (5/2) > 5 * (5/2)
x > 25/2
2. Simplify the inequality by multiplying and dividing:
5x / 10 > 25/2
x/2 > 25/2
3. Now we can graph the solution set on a number line. To do this, draw a number line and mark the point where x = 25/2, including an open circle at that point since the inequality is strictly greater than (>). Then, shade the region to the right of that point because the inequality symbol is "greater than".
---o--→
4. Finally, we can write the solution in interval notation. Since the inequality is x > 25/2, the solution set is all values of x greater than 25/2. In interval notation, this can be written as:
(25/2, ∞)
So, the solution set to the inequality 2/5 * x > 5 is (25/2, ∞) in interval notation.