1. If a < b and c < d and a, b, c, d are negative numbers. Which one of the following is always correct? a. a < d b. b < c c. a + b < c + d d. a + d < c + b e. ac > bd 2. Which of... 1. If a < b and c < d and a, b, c, d are negative numbers. Which one of the following is always correct? a. a < d b. b < c c. a + b < c + d d. a + d < c + b e. ac > bd 2. Which of the following is an integer number? a. 3.1 b. √2 c. 0 d. a, b, & c 3. Which of the following is not correct? a. |-2| = |2| b. |2 - 5| = |3| c. |5| + |-5| = 0 d. |8| = |4| |2| e. |2| = 2 4. The result of the given operations |2 - 3| - 2 - 1 is a. -4 b. -2 c. 0 d. 1 e. 2 5. Find the result of (2x - 2)^2 - 2(2x^2 - 4x + 1) Read more

Steps to Solve

1. Evaluate the Inequality Relations (Question 1)

Given that $a < b < c < d$ and all of these are negative numbers, we can analyze each option:

• Option a: $a < d$. This is true since $a < d$ is given.
• Option b: $b < c$. This is also true since $b < c$ is given.
• Option c: $a + b < c + d$. Since $a, b, c, d$ are both negative, $a + b$ will be a larger negative number than $c + d$, hence can be false.
• Option d: $a + d < c + b$. This could be true or false depending on the specific numbers, hence inconclusive.
• Option e: $ac > bd$. Since both products involve negative numbers, $ac$ could be greater than or less than $bd$ based on their values—they depend on the actual magnitudes.

Thus, the always true statement is a or b.

2. Identify an Integer (Question 2)

Now check each of the options for being an integer:

• Option a: $3.1$ is not an integer.
• Option b: $\sqrt{2}$ is not an integer.
• Option c: $0$ is an integer.
• Option d: a, b, & c includes non-integer values.

The integer is c. $0$.

3. Determine the Incorrect Statement (Question 3)

Evaluate the statements:

• Option a: $|-2| = |2|$. This is true since both expressions evaluate to $2$.
• Option b: $|2-5| = |3|$. This is false because $|2-5| = | -3| = 3$, but equals $3$, thus this works.
• Option c: $|5| + |-5| = 0$. This is false as $|5| + |-5| = 5 + 5 = 10$, not $0$.
• Option d: $|8| = |4| | 2|$. This is false as $|4| |2|$ is 8.
• Option e: $|2| = 2$. This is true.

The incorrect statement is c.

4. Evaluate the Expression (Question 4)

Simplify $|2 - 3 - 2 - 1|$:

1. Combine the numbers inside the absolute value: $$ 2 - 3 - 2 - 1 = -4 $$
2. Take the absolute value: $$ |-4| = 4 $$

Thus, the answer is none of the provided options match.

5. Find the Result: Expression (Question 5)

Calculate the expression:

$$(2x - 2)^2 - 2(2x^2 - 4x - 1)$$

Expanding the squared term and distributing:

1. Expand $(2x - 2)^2$: $$ (2x - 2)(2x - 2) = 4x^2 - 8x + 4 $$

2. Expand $-2(2x^2 - 4x - 1)$: $$ -2(2x^2 - 4x - 1) = -4x^2 + 8x + 2 $$

3. Combine the results: [ 4x^2 - 8x + 4 - 4x^2 + 8x + 2 = 6 ]

The final result for the expression is a. 6.