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2 years ago

Solve the following inequality.

Mathematics

1 answer:

Anika [276]2 years ago

8 0

Solving the inequality given algebraically, the solution of the inequality for the value of m is:

m < -4 OR m > 3

Given the following inequality,

$\frac{m - 2}{3} < -2 \\$

4m + 3 > 15

Let's solve algebraically for the value of m in both inequality statements given.

$\frac{m - 2}{3} < -2 \\$

Multiply both sides by 3

$\frac{m - 2}{3} \times 3 < -2 \times 3\\\\m - 2 < -6$

Add 2 to both sides

$m - 2 + 2 < -6 + 2\\\\m < -4$

4m + 3 > 15

Subtract 3 from each side

4m + 3 - 3 > 15 - 3

4m > 12

Divide both sides by 4

$\frac{4m}{4} > \frac{12}{4} \\\\$

m > 3

Therefore, solving the inequality given algebraically, the solution of the inequality for the value of m is:

m < -4 OR m > 3

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Answer:

A) probability the sum is 8 or 11= 4/21

B) probability that sum is 12 or less than 10 = 6/7

C) Probability that the sum is 3 or less than 3 = 2/21

D) Probability that the sum is 2 or 10 = 1/7

Step-by-step explanation:

Since we have the same probability of each event in each dice, the answer would be just to check the different outcomes, two dices, each with 1 to 6;

(1,1);(1,2);(1,3);(1,4);(1,5);(1,6);(2,2);(2,3);(2,4);(2,5);(2,6);(3,3);(3,4);(3,5);(3,6);(4,4);(4,5);(4,6);(5,5);(5,6);(6,6)

Thus, there are 21 possible outcomes.

Now,

A) probability that the sum is 8 or 11;

From the outcomes above, the number of outcomes that have a sum as 8 or 11 are;

(2,6) ; (3,5) ; (4,4) ; (5,6)

So,probability = 4/21

B) From the outcomes above, the number of outcomes that are 12 or less than 10 are;

(1,1);(1,2);(1,3);(1,4);(1,5);(1,6);(2,2);(2,3);(2,4);(2,5);(2,6);(3,3);(3,4);(3,5);(3,6);(4,4);(4,5);(6,6).

There are 18 possible outcomes.

So, probability that sum is 12 or less than 10 = 18/21 = 6/7

C)From the initial 21 outcomes, the number of outcomes that the sum is 3 or less than 3 are;(1,1);(1,2)

Thus,

Probability that the sum is 3 or less than 3 = 2/21

D) From the initial 21 outcomes, the number of outcomes that the sum is 2 or 10 are;

(1,1); (4,6) ; (5,5)

Thus,

Probability that the sum is 2 or 10 = 3/21 = 1/7

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