Solve the inequality. Graph the solution set and write it in interval notation.
2/9 * x > 5
Write the answer in interval notation
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(Use integers or fractions for any numbers in the expression)
To solve the inequality, we can start by multiplying both sides by 9/2 to isolate x:
(2/9)(9/2)x > (5)(9/2)
x > 45/2
This means that x must be greater than 45/2.
Now, we can graph the solution set. Since x is greater than 45/2, we would have an open circle at 45/2 and an arrow pointing to the right.
In interval notation, we write the solution set as (45/2, ∞). This indicates that x is greater than 45/2, and there is no specific upper bound.
To solve the inequality 2/9 * x > 5, we need to isolate the variable x.
First, we can multiply both sides of the inequality by the reciprocal of 2/9, which is 9/2:
9/2 * (2/9) * x > 5 * (9/2)
Simplifying this equation, we get:
x > 45/2
The solution to the inequality is x being greater than 45/2.
To graph the solution set, we can plot an open circle on the number line at 45/2 and shade everything to the right of it, as the inequality is strict (x > 45/2).
In interval notation, we write the solution as:
(45/2, ∞)
To solve the inequality 2/9 * x > 5, we can follow these steps:
Step 1: Multiply both sides of the inequality by the reciprocal of 2/9, which is 9/2. When multiplying or dividing both sides of an inequality by a negative number, remember to reverse the inequality sign.
(2/9 * x)*(9/2) > 5 * (9/2)
x > 45/2
Step 2: Simplify the right side of the inequality.
x > 22.5
Now that we have solved the inequality, let's graph the solution set.
To graph the solution set on a number line, we need to determine whether the inequality includes or excludes the endpoint, 22.5.
Since the inequality is "greater than," the endpoint is excluded. Therefore, we represent this inequality with an open circle on the number line at 22.5, indicating that it does not include 22.5.
o----->
|-------|
22.5
Next, we shade the region to the right of 22.5 since our inequality is "greater than."
Now let's write the answer in interval notation.
The solution set is (22.5, ∞), where the parenthesis indicates that 22.5 is not included, and ∞ represents all numbers greater than 22.5.