Which integer satisfies the equations 5m + 6 < 36 and m^2 > 9?

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Question

Here is the question : WHICH INTEGER SATISFIES THE EQUATIONS 5M + 6 < 36 AND M^2 > 9?

Option

Here is the option for the question :

  • 2
  • 4
  • 7
  • 9

The Answer:

And, the answer for the the question is :

4

Explanation:

Find a range for your responses by solving each problem independently. The variable m can be any number less than 6 by first subtracting 6 from both sides of the equation 5m + 6 36, and then dividing the result by 5. If you take the square root of both sides of the second equation, m2 > 9, then m can be any positive integer greater than 3. Since the correct answer must be between 3 and 6, we can eliminate 1 and 2 and leave only 4.

Which integer satisfies the equations 5m + 6 < 36 and m^2 > 9?’ width=’960′ height=’540′ /><!-- the_image --><br /> In mathematics, equations are an essential tool for solving problems. One type of equation is the inequality, which compares two values and determines whether they are equal or not. In this case, we are given two inequalities to solve: 5m + 6 < 36 and m^2 > 9. By finding the integer that satisfies both inequalities, we can solve the problem at hand.</p> <p>The first inequality, 5m + 6 < 36, can be simplified by subtracting 6 from both sides, giving us 5m < 30. Dividing both sides by 5 gives us m < 6. This tells us that any integer value of m that is less than 6 will satisfy the first inequality. The second inequality, m^2 > 9, can be simplified by taking the square root of both sides, giving us |m| > 3. This tells us that any integer value of m that is greater than 3 or less than -3 will satisfy the second inequality.</p> <p>To find the integer that satisfies both inequalities, we need to look for the intersection of the two sets of numbers that satisfy each inequality. In this case, the set of numbers that satisfy the first inequality is {m | m < 6}, and the set of numbers that satisfy the second inequality is {m | m > 3 or m < -3}. The intersection of these two sets is {m | 3 < m < 6}, which containsonly one integer value: 4. Therefore, the integer that satisfies both inequalities is 4. Plugging this value into the original equations, we get 5(4) + 6 = 26, which is indeed less than 36, and 4^2 = 16, which is indeed greater than 9. Thus, the answer to the problem is 4. Inequalities can be used to solve a wide range of problems in mathematics, from simple arithmetic to complex analysis. They are a useful tool for expressing relationships between variables and determining the set of values that satisfy certain conditions. By understanding how to solve inequalities, we can tackle a wide range of mathematical problems and gain a deeper understanding of the world around us. the integer that satisfies the equations 5m + 6 < 36 and m^2 > 9 is 4. This solution demonstrates the importance of understanding inequalities and how they can be used to solve mathematical problems. With this knowledge, we can tackle a wide range of problems and gain a deeper appreciation for the beauty and complexity of mathematics.</p> <div class=

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