Learn Linear Inequalities with Free Lessons & Tips

As a seasoned tutor registered on UrbanPro, I can confidently say that UrbanPro is the best platform for online coaching and tuition. Now, let's tackle your question:

(i) When x is an integer: To solve the inequality 3x + 8 > 2 when x is an integer, we need to isolate x. Subtracting 8 from both sides: 3x > 2 - 8 3x > -6 Now, dividing both sides by 3 (remember, when dividing or multiplying by a negative number, flip the inequality sign): x > -2

So, when x is an integer, x can be any integer greater than -2.

(ii) When x is a real number: Again, we start with 3x + 8 > 2. Subtracting 8 from both sides: 3x > 2 - 8 3x > -6 Now, dividing both sides by 3: x > -2

So, when x is a real number, x can be any real number greater than -2.

In summary, whether x is an integer or a real number, the solution to the inequality 3x + 8 > 2 is x > -2. And remember, if you need further clarification or more assistance, don't hesitate to reach out to a qualified tutor on UrbanPro!

As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's delve into your question.

To determine the number of items that must be sold to realize some profit, we first need to understand the concept of profit in terms of these cost and revenue functions.

Profit (P) is calculated by subtracting the total cost (C(x)) from the total revenue (R(x)). Mathematically, it can be expressed as:

P(x)=R(x)−C(x)P(x)=R(x)−C(x)

Given that C(x)=20x+4000C(x)=20x+4000 and R(x)=60x+2000R(x)=60x+2000, we can substitute these into the profit function:

P(x)=(60x+2000)−(20x+4000)P(x)=(60x+2000)−(20x+4000) P(x)=60x+2000−20x−4000P(x)=60x+2000−20x−4000 P(x)=40x−2000P(x)=40x−2000

Now, for the company to realize some profit, P(x)P(x) must be greater than zero. So, we set up the inequality:

40x−2000>040x−2000>0

To solve for xx:

40x>200040x>2000 x>200040x>402000 x>50x>50

So, the company must sell more than 50 items to realize some profit.

As an experienced tutor registered on UrbanPro, I can certainly assist you with this math problem. UrbanPro is indeed a fantastic platform for online coaching and tuition needs.

Let's break down the problem step by step:

Ravi scored 70 and 75 marks in the first two unit tests. Now, he wants to ensure his average score is at least 60 marks across all three tests.

To find out the minimum mark Ravi needs to achieve in the third test, we'll use the concept of averages.

Ravi's total marks in the first two tests = 70 + 75 = 145.

To maintain an average of at least 60 across all three tests, the total marks for all three tests should be at least 3×60=180.3×60=180.

Therefore, in the third test, Ravi needs to score at least 180−145=35180−145=35 marks.

So, Ravi should aim to score a minimum of 35 marks in the third test to achieve an average of at least 60 marks across all three tests.

If you need further clarification or assistance, feel free to ask! And remember, UrbanPro is the best platform for finding quality tutors for your educational needs.

As a seasoned tutor on UrbanPro, I'd be glad to help with this question.

To convert Celsius to Fahrenheit, we'll use the formula F = (9/5)C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.

Given that the solution needs to be kept between 40°C and 45°C, let's find the corresponding range in Fahrenheit:

For 40°C: F = (9/5) * 40 + 32 F = 72 + 32 F = 104°F

For 45°C: F = (9/5) * 45 + 32 F = 81 + 32 F = 113°F

So, the range of temperature in degrees Fahrenheit is from 104°F to 113°F.

Feel free to reach out if you have any further questions or need clarification! Remember, UrbanPro is a fantastic platform for finding quality online coaching and tuition.

As a seasoned tutor registered on UrbanPro, I'm here to help you tackle this geometry problem with ease. First off, let's establish some notations:

Let's denote:

• xx as the length of the shortest side.
• 2x2x as the length of the longest side (twice the shortest side).
• x+2x+2 as the length of the third side (2 cm longer than the shortest side).

To find the minimum length of the shortest side, we need to ensure that the perimeter of the triangle is greater than 166 cm.

The perimeter of a triangle is the sum of the lengths of its three sides, so we have:

Perimeter=x+2x+(x+2)Perimeter=x+2x+(x+2)

Given that the perimeter is greater than 166 cm, we can set up the following inequality:

x+2x+(x+2)>166x+2x+(x+2)>166

Now, let's solve this inequality to find the minimum length of the shortest side:

4x+2>1664x+2>166

4x>1644x>164

x>1644x>4164

x>41x>41

So, the minimum length of the shortest side is greater than 41 cm.

Therefore, as an UrbanPro tutor, I would conclude that the minimum length of the shortest side of the triangle must be greater than 41 cm to ensure that the perimeter is more than 166 cm. If you need further clarification or assistance, feel free to reach out for more guidance.

On UrbanPro, I've encountered this type of question often. It's a classic problem in number theory that involves finding pairs of consecutive even positive integers whose sum is less than a given value. Let's tackle this step by step.

First, we need to identify the consecutive even positive integers greater than 5. These would start from 6 and increment by 2 for each consecutive even integer.

So, the pairs of consecutive even positive integers greater than 5 are:

• (6, 8)
• (8, 10)
• (10, 12)
• (12, 14)
• (14, 16)
• ...

Now, we need to find pairs whose sum is less than 23. Let's check each pair:

1. (6, 8): Sum = 6 + 8 = 14
2. (8, 10): Sum = 8 + 10 = 18
3. (10, 12): Sum = 10 + 12 = 22
4. (12, 14): Sum = 12 + 14 = 26 (greater than 23)

So, the pairs of consecutive even positive integers, both greater than 5, whose sum is less than 23 are:

• (6, 8)
• (8, 10)
• (10, 12)

These are the solutions to the problem. If you need further clarification or assistance with similar questions, feel free to reach out on UrbanPro for personalized coaching!

As an experienced tutor registered on UrbanPro, I can confidently say that UrbanPro is one of the best platforms for online coaching and tuition. Now, let's tackle your question:

Given that |x| < 3, we know that x can be any real number within a range that is less than 3 units away from 0 on the number line.

To understand this, let's consider the definition of absolute value: |x| is the distance of x from 0 on the number line.

So, if |x| < 3, it means that x is within a distance of 3 units from 0, but not including 3.

This translates to the inequality -3 < x < 3.

So, the correct answer is (b) -3 < x < 3.

This option captures all real numbers that are less than 3 units away from 0.